Edgar Filing: FIRST TRUST ENERGY INFRASTRUCTURE FUND

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT INVESTMENT
COMPANIES

Investment Company Act file number 811-22528
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First Trust Energy Infrastructure Fund
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(Exact name of registrant as specified in charter)

120 East Liberty Drive, Suite 400
Wheaton, IL 60187
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(Address of principal executive offices) (Zip code)

W. Scott Jardine, Esq.
First Trust Portfolios L.P.
120 East Liberty Drive, Suite 400
Wheaton, IL 60187
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(Name and address of agent for service)

registrant's telephone number, including area code: 630-765-8000
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Date of fiscal year end: November 30
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Date of reporting period: May 31, 2013
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Form N-CSR is to be used by management investment companies to file reports with
the Commission not later than 10 days after the transmission to stockholders of
any report that is required to be transmitted to stockholders under Rule 30e-1
under the Investment Company Act of 1940 (17 CFR 270.30e-1). The Commission may
use the information provided on Form N-CSR in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-CSR,
and the Commission will make this information public. A registrant is not
required to respond to the collection of information contained in Form N-CSR
unless the Form displays a currently valid Office of Management and Budget
("OMB") control number. Please direct comments concerning the accuracy of the
information collection burden estimate and any suggestions for reducing the
burden to Secretary, Securities and Exchange Commission, 100 F Street, NE,
Washington, DC 20549. The OMB has reviewed this collection of information under
the clearance requirements of 44 U.S.C. ss. 3507.

ITEM 1. REPORTS TO STOCKHOLDERS.

The Report to Shareholders is attached herewith.

FIRST TRUST
-------------------
E N E R G Y
INFRASTRUCTURE
-------------------
FUND

SEMI-ANNUAL
REPORT
For the Six Months
Ended May 31, 2013

FIRST TRUST

ENERGY INCOME PARTNERS, LLC

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TABLE OF CONTENTS
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FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
SEMI-ANNUAL REPORT
MAY 31, 2013

Shareholder Letter........................................................... 1
At A Glance.................................................................. 2
Portfolio Commentary......................................................... 3
Portfolio of Investments..................................................... 5
Statement of Assets and Liabilities.......................................... 9
Statement of Operations...................................................... 10
Statements of Changes in Net Assets.......................................... 11
Statement of Cash Flows...................................................... 12
Financial Highlights......................................................... 13
Notes to Financial Statements................................................ 14
Additional Information....................................................... 20

CAUTION REGARDING FORWARD-LOOKING STATEMENTS

This report contains certain forward-looking statements within the meaning of
the Securities Act of 1933, as amended, and the Securities Exchange Act of 1934,
as amended. Forward-looking statements include statements regarding the goals,
beliefs, plans or current expectations of First Trust Advisors L.P. ("First
Trust" or the "Advisor") and/or Energy Income Partners, LLC ("EIP" or the
"Sub-Advisor") and their respective representatives, taking into account the
information currently available to them. Forward-looking statements include all
statements that do not relate solely to current or historical fact. For example,
forward-looking statements include the use of words such as "anticipate,"
"estimate," "intend," "expect," "believe," "plan," "may," "should," "would" or
other words that convey uncertainty of future events or outcomes.

Forward-looking statements involve known and unknown risks, uncertainties and
other factors that may cause the actual results, performance or achievements of
the First Trust Energy Infrastructure Fund (the "Fund") to be materially
different from any future results, performance or achievements expressed or
implied by the forward-looking statements. When evaluating the information
included in this report, you are cautioned not to place undue reliance on these
forward-looking statements, which reflect the judgment of the Advisor and/or
Sub-Advisor and their respective representatives only as of the date hereof. We
undertake no obligation to publicly revise or update these forward-looking
statements to reflect events and circumstances that arise after the date hereof.

PERFORMANCE AND RISK DISCLOSURE

There is no assurance that the Fund will achieve its investment objective. The
Fund is subject to market risk, which is the possibility that the market values
of securities owned by the Fund will decline and that the value of the Fund
shares may therefore be less than what you paid for them. Accordingly, you can
lose money by investing in the Fund. See "Risk Considerations" in the Additional
Information section of this report for a discussion of certain other risks of
investing in the Fund.

Performance data quoted represents past performance, which is no guarantee of
future results, and current performance may be lower or higher than the figures
shown. For the most recent month-end performance figures, please visit
http://www.ftportfolios.com or speak with your financial advisor. Investment
returns, net asset value and common share price will fluctuate and Fund shares,
when sold, may be worth more or less than their original cost.

HOW TO READ THIS REPORT

This report contains information that may help you evaluate your investment. It
includes details about the Fund and presents data and analysis that provide
insight into the Fund's performance and investment approach.

By reading the portfolio commentary by the portfolio management team of the
Fund, you may obtain an understanding of how the market environment affected the
Fund's performance. The statistical information that follows may help you
understand the Fund's performance compared to that of relevant market
benchmarks.

It is important to keep in mind that the opinions expressed by personnel of EIP
are just that: informed opinions. They should not be considered to be promises
or advice. The opinions, like the statistics, cover the period through the date
on the cover of this report. The risks of investing in the Fund are spelled out
in the prospectus, the statement of additional information, this report and
other Fund regulatory filings.

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SHAREHOLDER LETTER
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FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
SEMI-ANNUAL LETTER FROM THE CHAIRMAN AND CEO
MAY 31, 2013

Dear Shareholders:

I am pleased to present you with the semi-annual report for your investment in
First Trust Energy Infrastructure Fund (the "Fund").

The report you hold contains detailed information about your investment, a
portfolio commentary from the Fund's management team that provides a recap of
the period, a performance analysis and a market and Fund outlook. Additionally,
you will find the Fund's financial statements for the period this report covers.
I encourage you to read this document and discuss it with your financial
advisor. A successful investor is also typically a knowledgeable one, as we have
found to be the case at First Trust Advisors L.P. ("First Trust").

The six months covered by this report have been more positive for the U.S.
markets. In fact, the S&P 500 Index, as measured on a total return basis, rose
16.43% during the period, and many economists and investors have felt positive
about the current market environment. Of course, past performance can never be
an indicator of future performance. As I have written many times, First Trust
believes that staying invested in quality products through up and down markets
and having a long-term horizon can help investors reach their financial goals.

First Trust offers a variety of products that we believe could fit many
financial plans to help investors seeking long-term investment success. We
encourage you to talk to your advisor about the other investments First Trust
offers that might also fit your financial goals and to discuss those goals with
your advisor regularly so that he or she can help keep you on track.

First Trust will continue to make available up-to-date information about your
investments so you and your financial advisor are current on any First Trust
investments you own. We value our relationship with you, and thank you for the
opportunity to assist you in achieving your financial goals. I look forward to
the remainder of 2013 and to the next edition of your Fund's report.

Sincerely,

/s/ James A. Bowen

James A. Bowen
Chairman of the Board of Trustees and
Chief Executive Officer of First Trust Advisors L.P.

Page 1

FIRST TRUST ENERGY INFRASTRUCTURE FUND
"AT A GLANCE"
AS OF MAY 31, 2013 (UNAUDITED)

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FUND STATISTICS
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Symbol on New York Stock Exchange FIF
Common Share Price $23.08
Common Share Net Asset Value ("NAV") $23.86
Premium (Discount) to NAV (3.27)%
Net Assets Applicable to Common Shares $418,676,706
Current Monthly Distribution per Common Share (1) $0.1100
Current Annualized Distribution per Common Share $1.3200
Current Distribution Rate on Closing Common Share Price (2) 5.72%
Current Distribution Rate on NAV (2) 5.53%
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COMMON SHARE PRICE & NAV (WEEKLY CLOSING PRICE)
------------------------------------------------------------------
Common Share Price NAV
11/12 21.26 22.74
21.57 22.47
21.40 22.40
21.94 22.19
20.70 21.47
12/12 20.43 20.93
22.19 22.34
22.10 22.53
22.35 22.87
1/13 22.32 23.13
22.64 23.35
22.73 23.37
23.00 23.34
2/13 22.84 23.38
23.61 23.38
23.05 23.78
22.87 23.87
23.07 24.38
3/13 23.83 24.94
23.36 24.48
24.69 24.96
24.23 24.94
4/13 24.79 25.11
24.70 25.02
25.32 25.26
25.21 25.35
24.75 25.07
5/13 23.08 23.86

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PERFORMANCE
------------------------------------------------------------------------------------------------------
Average Annual
Total Return
---------------------
6 Months Ended 1 Year Ended Inception (9/27/2011)
5/31/2013 5/31/2013 to 5/31/2013

FUND PERFORMANCE (3)
NAV 13.24% 21.31% 23.95%
Market Value 16.72% 26.17% 18.23%

INDEX PERFORMANCE
Philadelphia Stock Exchange Utility Index 8.25% 7.02% 9.04%
Alerian MLP Total Return Index 14.68% 28.61% 22.76%
Blended Benchmark (4) 11.63% 17.63% 16.05%
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% OF TOTAL
INDUSTRY CLASSIFICATION INVESTMENTS
----------------------------------------------------------
Pipelines 51.9%
Electric Power 33.6
Propane 5.4
Coal 2.8
Marine 2.7
Natural Gas Utility 1.4
Gathering & Processing 0.8
Other 1.4
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Total 100.0%
======

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% OF TOTAL
TOP 10 HOLDINGS INVESTMENTS
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Enbridge Energy Management, LLC 8.5%
Kinder Morgan Management, LLC 7.7
Southern (The) Co. 5.0
Kinder Morgan, Inc. 4.2
NextEra Energy, Inc. 4.1
Dominion Resources, Inc. 3.7
Duke Energy Corp. 3.4
Spectra Energy Corp. 3.3
TransCanada Corp. 3.2
Northeast Utilities 3.0
----------------------------------------------------------
Total 46.1%
======

(1) Most recent distribution paid or declared through 5/31/2013. Subject to
change in the future.

(2) Distribution rates are calculated by annualizing the most recent
distribution paid or declared through the report date and then dividing by
Common Share price or NAV, as applicable, as of 5/31/2013. Subject to
change in the future.

(3) Total return is based on the combination of reinvested dividend, capital
gain and return of capital distributions, if any, at prices obtained by
the Dividend Reinvestment Plan and changes in NAV per share for NAV
returns and changes in Common Share price for market value returns. Total
returns do not reflect sales load and are not annualized for periods less
than one year. Past performance is not indicative of future results.

(4) The blended benchmark consists of the following: Philadelphia Stock
Exchange Utility Index (50%) and Alerian MLP Total Return Index (50%).

Page 2

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PORTFOLIO COMMENTARY
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FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
SEMI-ANNUAL REPORT
MAY 31, 2013

SUB-ADVISOR

ENERGY INCOME PARTNERS, LLC

Energy Income Partners, LLC ("EIP"), located in Westport, CT, was founded in
2003 to provide professional asset management services in the area of
energy-related master limited partnerships ("MLPs") and other high-payout
securities such as pipeline companies, power utilities and Canadian income
trusts and their successor companies (collectively, "Canadian Income Equities").
EIP mainly focuses on investments in energy-related infrastructure assets such
as pipelines, power transmission, petroleum storage and terminals that receive
fee-based or regulated income from their corporate customers. EIP manages or
supervises approximately $3.9 billion of assets as of May 31, 2013. Private
funds advised by EIP include a partnership for U.S. high net worth individuals
and a master-and-feeder fund for institutions. EIP also manages separately
managed accounts and provides its model portfolio to unified managed accounts.
EIP is a registered investment advisor and serves as a sub-advisor to two
closed-end management investment companies in addition to the First Trust Energy
Infrastructure Fund ("FIF" or the "Fund") and an actively managed
exchange-traded fund (ETF).

PORTFOLIO MANAGEMENT TEAM

JAMES J. MURCHIE EVA PAO
PORTFOLIO MANAGER CO-PORTFOLIO MANAGER
FOUNDER AND CEO OF PRINCIPAL OF
ENERGY INCOME PARTNERS, LLC ENERGY INCOME PARTNERS, LLC

COMMENTARY

FIRST TRUST ENERGY INFRASTRUCTURE FUND

The investment objective of the Fund is to seek a high level of total return
with an emphasis on current distributions paid to shareholders. The Fund pursues
its objective by investing primarily in securities of companies engaged in the
energy infrastructure sector. These companies principally include
publicly-traded master limited partnerships ("MLPs"), MLP affiliates, Canadian
Income Equities, pipeline companies, utilities and other infrastructure related
companies that derive at least 50% of their revenues from operating or providing
services in support of infrastructure assets such as pipelines, power
transmission and petroleum and natural gas storage in the petroleum, natural gas
and power generation industries (collectively, "Energy Infrastructure
Companies"). Under normal market conditions, the Fund invests at least 80% of
its managed assets (total asset value of the Fund minus the sum of the Fund's
liabilities other than the principal amount of borrowing) in securities of
Energy Infrastructure Companies. There can be no assurance that the Fund's
investment objective will be achieved. The Fund may not be appropriate for all
investors.

MARKET RECAP

As measured by the Alerian MLP Total Return Index ("AMZX") and the Philadelphia
Stock Exchange Utility Index ("UTY"), the total return for energy-related MLPs
and utilities over the semi-annual period ended May 31, 2013, was 14.68% and
8.25%, respectively. These figures are according to data collected from several
sources, including Alerian Capital Management and Bloomberg. While in the short
term, share appreciation of Energy Infrastructure Companies can be volatile, we
believe that over the longer term, share appreciation will approximate growth in
per share quarterly cash distributions and dividends. Over the last 10 years,
growth in per share MLP distributions and utility dividends has averaged 6.8%
and 5.2%, respectively. Over the last 12 months, the cash distributions of MLPs
and utilities increased by about 7.8% and 6.5%, respectively (Source: Alerian
Capital Management and Bloomberg).

PERFORMANCE ANALYSIS

On a Net Asset Value ("NAV") basis, the Fund provided a total return(1) of
13.24%, including the reinvestment of dividends, for the semi-annual period
ended May 31, 2013. This compares, according to collected data, to a total
return of 11.63% for the average of the two benchmarks (14.68% for AMZX and
8.25% UTY). Unlike the Fund, the indices do not incur fees and expenses. On a
market value basis, the Fund had a total return, including the reinvestment of
dividends, of 16.72% for the semi-annual period ended May 31, 2013. The Fund's

(1) Total return is based on the combination of reinvested dividend, capital
gain and return of capital distributions, if any, at prices obtained by
the Dividend Reinvestment Plan and changes in NAV per share for NAV
returns and changes in Common Share price for market value returns. Total
returns do not reflect sales load and are not annualized for periods less
than one year. Past performance is not indicative of future results.

Page 3

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PORTFOLIO COMMENTARY (CONTINUED)
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discount to NAV narrowed over the course of the period. On May 31, 2013, the
Fund was priced at $23.08, while the NAV was $23.86, a discount of 3.27%. On
November 30, 2012, the Fund was priced at $21.34, while the NAV was $22.74, a
discount of 6.16%.

The Fund declared regular monthly Common Share distributions of $0.1085 per
share for December 2012 and $0.11 per share for each month from January through
May 2013. In addition, the Fund declared a short-term capital gain of $0.988 per
share and a long-term capital gain of $0.095 per share in December 2012. The
outperformance of the Fund's NAV relative to the 11.63% average of the AMZX and
UTY benchmarks was driven by outperforming positions that made up a larger
portion of the Fund than of the respective benchmarks. The companies held by the
Fund tended to have non-cyclical and/or regulated businesses like pipelines,
power transmission and distribution and storage terminals, while the benchmarks
included numerous companies that operated businesses whose earnings and cash
flows were more cyclical. This approach had a favorable impact on performance
relative to the benchmarks over the reporting period.

An important factor that affected the return of the Fund was its use of
financial leverage through the use of a line of credit. The Fund has a committed
facility agreement with The Bank of Nova Scotia with a maximum commitment amount
of $165,000,000. The Fund uses leverage because its managers believe that, over
time, leverage can enhance total return for common shareholders. However, the
use of leverage can also increase the volatility of the NAV and therefore
volatility of the share price. For example, if the prices of securities held by
the Fund decline, the effect of changes in Common Share NAV and common
shareholder total return is magnified by the use of leverage, and conversely,
leverage may enhance Common Share returns during periods when the prices of
securities held by the Fund generally are rising. Unlike the Fund, AMZX and UTY
are not leveraged. Leverage had a positive impact on the performance of the Fund
over this reporting period.

MARKET AND FUND OUTLOOK

The MLP asset class has experienced 7 IPOs so far in 2013, as of May 31, 2013.
There was a healthy level of secondary financing activity for MLPs during the
reporting period, as they continued to fund their ongoing investments in new
pipelines, processing and storage facilities. There have been 33 secondary
equity offerings in 2013 through May 31, 2013, which raised $9.6 billion in
proceeds. In 2012, there were a total of 67 secondary equity offerings for MLPs
that raised $25.0 billion. MLPs also found access to the public debt markets,
raising $7.1 billion in 7 offerings in 2013 through May 31, 2013. This compares
to $18.2 billion in 2012 (Source: Barclays Capital). The combination of equity
and debt raised in 2012 of approximately $43 billion represents approximately
11% of the roughly $389 billion MLP market cap.

Capital spending for utilities continues to increase. As measured by UTY,
capital expenditures for the power utility industry have grown from $77 billion
in 2011 to $80 billion in 2012. This growth in expenditures is in response to
needs such as reliability, interconnection, modernization and growing demand.
These capital investments are supported, in part, by federal and state
regulation, which allows companies to recoup investments made in their rate
structure.

The Fund continues to aim to be invested in Energy Infrastructure Companies with
mostly non-cyclical cash flows, investment-grade ratings, conservative balance
sheets, modest and/or flexible organic growth commitments and liquidity on their
revolving lines of credit. Since the Fund invests in securities that tend to
have high dividend payout ratios (as measured versus earnings), securities with
unpredictable cyclical cash flows make them a poor fit with the portfolio, in
the opinion of the Sub-Advisor. While there are some businesses within the
Fund's portfolio whose cash flows are cyclical, they are usually small and
analyzed in the context of each company's financial and operating leverage and
payout ratio.

MLPs continue to play an integral role in the restructuring of more diversified
energy conglomerates. This restructuring includes the creation by these more
diversified conglomerates of MLP subsidiaries that contain assets such as
pipelines and storage terminals. It also includes the divestiture by some of the
parent companies of most or all of their cyclical businesses, leaving the parent
company looking very similar to an old-fashioned pipeline utility with a large
holding in a subsidiary MLP. Diversified energy conglomerates are doing this so
that their regulated infrastructure assets with predictable cash flows may be
better valued by the market, resulting in a better financing tool to raise
capital for the new energy infrastructure projects related to the rapid growth
of North American oil and gas production and the need to upgrade the power grid.

In the opinion of the Sub-Advisor, the total return proposition of owning
energy-related infrastructure MLPs has been and continues to be their yield plus
their growth in dividends. The yield of the MLPs, weighted by market
capitalization, on May 31, 2013, was 5.87% based on AMZX, and for utilities, was
4.17%, as measured by UTY. The growth in the quarterly cash distributions that
make up this yield has averaged 6.8% annually over the last ten years for MLPs
and 5.2% for utilities. While it is uncertain what these growth rates will be in
the future, in the opinion of the Sub-Advisor, growth will continue to be driven
by three factors: 1) modest increases in volume growth from both demand for
energy and increases in North American oil and gas production; 2) inflation,
cost escalators and cost pass-throughs in pipeline and power transmission
tariffs and contracts; and 3) accretion from profitable capital projects and
acquisitions.

Page 4

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS
MAY 31, 2013 (UNAUDITED)

SHARES/
UNITS DESCRIPTION VALUE
------------ -------------------------------------------------- --------------
COMMON STOCKS - 100.2%

ELECTRIC UTILITIES - 28.6%
285,800 Duke Energy Corp. (a) ............................ $ 19,128,594
214,400 Emera, Inc. (CAD) (a) ............................ 7,293,840
338,650 Exelon Corp....................................... 10,613,291
170,800 Fortis, Inc. (CAD) (a) ........................... 5,438,252
108,600 ITC Holdings Corp. (a) ........................... 9,401,502
303,300 NextEra Energy, Inc............................... 22,935,546
403,600 Northeast Utilities (a) .......................... 16,818,012
636,900 Southern (The) Co. (a) ........................... 27,959,910
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119,588,947
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GAS UTILITIES - 7.8%
50,800 Atmos Energy Corp. (a) ........................... 2,144,776
119,385 Laclede Group, Inc. (a) .......................... 5,650,492
375,500 Questar Corp...................................... 9,128,405
415,479 UGI Corp. (a) .................................... 15,867,143
-------------
32,790,816
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MULTI-UTILITIES - 16.4%
51,600 ATCO, Ltd. (CAD) (a) ............................. 4,628,695
54,500 Canadian Utilities, Ltd. (CAD) (a) ............... 4,000,960
259,600 Centerpoint Energy, Inc. (a) ..................... 6,017,528
366,900 Dominion Resources, Inc........................... 20,748,195
237,000 National Grid PLC, ADR (a) ....................... 14,115,720
329,400 NiSource, Inc..................................... 9,463,662
34,000 Sempra Energy (a) ................................ 2,764,200
175,100 Wisconsin Energy Corp. (a) ....................... 7,145,831
-------------
68,884,791
-------------
OIL, GAS & CONSUMABLE FUELS - 47.4%
1,599,425 Enbridge Energy Management, LLC (a) (b) .......... 47,566,906
508,600 Enbridge Income Fund Holdings, Inc. (CAD) (a) .... 12,406,553
258,569 Enbridge, Inc. (a) ............................... 11,172,766
99,300 Keyera Corp. (CAD) (a) ........................... 5,737,227
530,079 Kinder Morgan Management, LLC (a) (b) ............ 43,053,016
616,500 Kinder Morgan, Inc. (a) .......................... 23,414,670
292,100 Pembina Pipeline Corp. (CAD) (a) ................. 9,134,200
594,450 Spectra Energy Corp. (a) ......................... 18,172,337
386,400 TransCanada Corp. (a) ............................ 17,716,440
281,900 Williams Cos., Inc................................ 9,917,242
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198,291,357
-------------
TOTAL COMMON STOCKS .............................. 419,555,911
(Cost $390,288,163) -------------

MASTER LIMITED PARTNERSHIPS - 32.9%

GAS UTILITIES - 3.4%
192,764 AmeriGas Partners, L.P. (a) ...................... 9,059,908
110,000 Suburban Propane Partners, L.P. (a) .............. 5,196,400
-------------
14,256,308
-------------

See Notes to Financial Statements Page 5

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS (CONTINUED)
MAY 31, 2013 (UNAUDITED)

SHARES/
UNITS DESCRIPTION VALUE
------------ -------------------------------------------------- --------------
MASTER LIMITED PARTNERSHIPS (CONTINUED)

OIL, GAS & CONSUMABLE FUELS - 29.5%
37,000 Access Midstream Partners, L.P. (a) .............. $ 1,591,740
47,000 Alliance GP Holdings, L.P. (a) ................... 2,995,310
139,715 Alliance Resource Partners, L.P. (a) ............. 10,098,600
192,200 El Paso Pipeline Partners, L.P. (a) .............. 7,897,498
100,000 Energy Transfer Equity, L.P. (a) ................. 5,716,000
176,400 Energy Transfer Partners, L.P. (a) ............... 8,574,804
145,600 Enterprise Products Partners, L.P. (a) ........... 8,647,184
37,700 EQT Midstream Partners, L.P. (a) ................. 1,842,022
168,876 Holly Energy Partners, L.P. (a) .................. 6,072,781
112,600 Magellan Midstream Partners, L.P. (a) ............ 5,854,074
80,400 MPLX, L.P. (a) ................................... 2,985,252
105,239 Natural Resource Partners, L.P. (a) .............. 2,341,568
103,472 NGL Energy Partners, L.P. (a) .................... 2,880,661
154,200 ONEOK Partners, L.P. (a) ......................... 7,981,392
129,886 Plains All American Pipeline, L.P. (a) ........... 7,296,996
235,500 Spectra Energy Partners, L.P. (a) ................ 8,386,155
205,095 TC Pipelines, L.P. (a) ........................... 8,935,989
354,628 Teekay LNG Partners, L.P. (a) .................... 15,213,541
190,362 TransMontaigne Partners, L.P. (a) ................ 7,993,300
-------------
123,304,867
-------------
TOTAL MASTER LIMITED PARTNERSHIPS ................ 137,561,175
(Cost $113,163,653) -------------

TOTAL INVESTMENTS - 133.1% ....................... 557,117,086
(Cost $503,451,816) (c) -------------

NUMBER OF
CONTRACTS DESCRIPTION VALUE
------------ -------------------------------------------------- --------------
CALL OPTIONS WRITTEN - (0.4%)

Centerpoint Energy, Inc. Call
500 @ $25.00 due August 2013 ......................... (17,500)
-------------
Dominion Resources, Inc. Calls
2,849 @ 62.50 due June 2013 ........................... (8,547)
270 @ 50.00 due July 2013 ........................... (179,550)
550 @ 62.50 due July 2013 ........................... (4,400)
-------------
(192,497)
-------------
Duke Energy Corp. Call
1,000 @ 72.50 due October 2013 ........................ (80,000)
-------------
Enbridge, Inc. Calls
700 @ 45.00 due July 2013 ........................... (24,500)
375 @ 50.00 due January 2014 ........................ (8,625)
-------------
(33,125)
-------------
Exelon Corp. Calls
2,786 @ 39.00 due July 2013 ........................... (8,358)
600 @ 40.00 due October 2013 ........................ (3,000)
-------------
(11,358)
-------------

Page 6 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS (CONTINUED)
MAY 31, 2013 (UNAUDITED)

NUMBER OF
CONTRACTS DESCRIPTION VALUE
------------ -------------------------------------------------- --------------
CALL OPTIONS WRITTEN (CONTINUED)

Kinder Morgan, Inc. Calls
1,600 @ $40.00 due June 2013 ........................... $ (19,200)
500 @ 40.00 due September 2013 ...................... (38,500)
1,400 @ 42.50 due September 2013 ...................... (32,200)
-------------
(89,900)
-------------
Nextera Energy, Inc. Calls
2,125 @ 75.00 due June 2013 ........................... (467,500)
908 @ 82.50 due June 2013 ........................... (1,816)
-------------
(469,316)
-------------
NiSource, Inc. Calls
1,078 @ 32.00 due June 2013 ........................... (3,234)
916 @ 30.00 due July 2013 ........................... (20,610)
1,000 @ 31.00 due July 2013 ........................... (8,000)
-------------
(31,844)
-------------
Northeast Utilities Call
900 @ 45.00 due October 2013 ........................ (38,250)
-------------
Questar Corp. Calls
554 @ 25.00 due July 2013 ........................... (22,160)
1,874 @ 26.00 due July 2013 ........................... (28,110)
500 @ 26.00 due October 2013 ........................ (25,000)
791 @ 27.00 due October 2013 ........................ (19,775)
-------------
(95,045)
-------------
Southern (The) Co. Calls
2,422 @ 47.00 due August 2013 ......................... (44,807)
995 @ 49.00 due August 2013 ......................... (5,970)
-------------
(50,777)
-------------
Spectra Energy Corp. Calls
1,006 @ 29.00 due June 2013 ........................... (173,535)
1,000 @ 30.00 due June 2013 ........................... (120,000)
1,350 @ 31.00 due June 2013 ........................... (47,250)
767 @ 33.00 due September 2013 ...................... (30,680)
800 @ 34.00 due September 2013 ...................... (20,000)
-------------
(391,465)
-------------
TransCanada Corp. Calls
333 @ 55.00 due August 2013 ......................... (3,330)
400 @ 50.00 due November 2013 ....................... (24,000)
-------------
(27,330)
-------------
Williams (The) Cos., Inc. Calls
918 @ 37.00 due June 2013 ........................... (18,360)
582 @ 38.00 due June 2013 ........................... (5,238)
352 @ 40.00 due July 2013 ........................... (4,224)
340 @ 38.00 due August 2013 ......................... (20,400)
620 @ 39.00 due August 2013 ......................... (26,660)
-------------
(74,882)
-------------

See Notes to Financial Statements Page 7

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS (CONTINUED)
MAY 31, 2013 (UNAUDITED)

NUMBER OF
CONTRACTS DESCRIPTION VALUE
------------ -------------------------------------------------- --------------
CALL OPTIONS WRITTEN (CONTINUED)

Wisconsin Energy Corp. Call
1,000 @ $45.00 due October 2013 ........................ $ (32,500)
-------------
TOTAL CALL OPTIONS WRITTEN ....................... (1,635,789)
(Premiums received $1,536,011) -------------

OUTSTANDING LOAN - (34.9%) ....................... (145,900,000)
NET OTHER ASSETS AND LIABILITIES - 2.2% .......... 9,095,409
-------------
NET ASSETS - 100.0% .............................. $ 418,676,706
=============

-----------------------------

(a) All or a portion of this security serves as collateral on the outstanding
loan.

(b) Non-income producing security which pays in-kind distributions.

(c) Aggregate cost for financial reporting purposes, which approximates the
aggregate cost for federal income tax purposes. As of May 31, 2013, the
aggregate gross unrealized appreciation for all securities in which there
was an excess of value over tax cost was $62,377,131 and the aggregate
gross unrealized depreciation for all securities in which there was an
excess of tax cost over value was $8,711,861.

ADR American Depositary Receipt

CAD Canadian Dollar - Security is denominated in Canadian Dollars and is
translated into U.S. Dollars based upon the current exchange rate.

OPEN SWAP AGREEMENT AT MAY 31, 2013:
UNREALIZED
LONG TOTAL RETURN NOTIONAL APPRECIATION/
EQUITY SWAP COUNTERPARTY PAY RATE AMOUNT EXPIRATION DATE (DEPRECIATION)
--------------------------------------------------------------------------------------------------------------

Credit Suisse 1 month LIBOR +
Inter Pipeline Fund International 40 basis points $ 8,823,956 02/24/14 $ (587,712)

-----------------------------

VALUATION INPUTS

A summary of the inputs used to value the Fund's investments as of May 31, 2013,
is as follows (see Note 2A - Portfolio Valuation in the Notes to Financial
Statements):

ASSETS TABLE

LEVEL 2 LEVEL 3
TOTAL LEVEL 1 SIGNIFICANT SIGNIFICANT
VALUE AT QUOTED OBSERVABLE UNOBSERVABLE
5/31/2013 PRICES INPUTS INPUTS
-------------- -------------- -------------- --------------
Common Stocks*....................................... $ 419,555,911 $ 419,555,911 $ -- $ --
Master Limited Partnerships*......................... 137,561,175 137,561,175 -- --
-------------- -------------- -------------- --------------
Total Investments.................................... $ 557,117,086 $ 557,117,086 $ -- $ --
============== ============== ============== ==============

LIABILITIES TABLE
LEVEL 2 LEVEL 3
TOTAL LEVEL 1 SIGNIFICANT SIGNIFICANT
VALUE AT QUOTED OBSERVABLE UNOBSERVABLE
5/31/2013 PRICES INPUTS INPUTS
-------------- -------------- -------------- --------------
Call Options Written........................... $ (1,635,789) $ (1,635,789) $ -- $ --
Total Return Equity Swap....................... (587,712) -- (587,712) --
-------------- -------------- -------------- --------------
Total.......................................... $ (2,223,501) $ (1,635,789) $ (587,712) $ --
============== ============== ============== ==============

* See Portfolio of Investments for industry breakout.

All transfers in and out of the Levels during the period are assumed to be
transferred on the last day of the period at their current value. There were no
transfers between Levels at May 31, 2013.

Page 8 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENT OF ASSETS AND LIABILITIES
MAY 31, 2013 (UNAUDITED)

ASSETS:

Investments, at value
(Cost $503,451,816) $ 557,117,086
Cash 6,288,317
Cash segregated as collateral for open swaps 2,700,000
Receivables:
Dividends.................................................................................. 1,500,646
Interest................................................................................... 567
Prepaid expenses 23,176
-------------
Total Assets............................................................................... 567,629,792
-------------
LIABILITIES:
Outstanding loan 145,900,000
Options written, at value (Premiums received $1,536,011) 1,635,789
Swap contracts 587,712
Payables:
Investment advisory fees................................................................... 501,715
Interest and fees on loan.................................................................. 100,402
Investment securities purchased............................................................ 85,722
Administrative fees........................................................................ 42,239
Audit and tax fees......................................................................... 31,964
Custodian fees............................................................................. 29,978
Legal fees................................................................................. 16,065
Printing fees.............................................................................. 7,577
Trustees' fees and expenses................................................................ 6,385
Transfer agent fees........................................................................ 5,092
Financial reporting fees................................................................... 771
Other liabilities 1,675
-------------
Total Liabilities.......................................................................... 148,953,086
-------------
NET ASSETS $ 418,676,706
=============

NET ASSETS CONSIST OF:
Paid-in capital $ 334,446,324
Par value 175,502
Accumulated net investment income (loss) (4,641,541)
Accumulated net realized gain (loss) on investments, written options, swaps and foreign
currency transactions 35,720,476

Net unrealized appreciation (depreciation) on investments, written options, swaps and
foreign currency translation 52,975,945
-------------
NET ASSETS $ 418,676,706
=============
NET ASSET VALUE, per Common Share (par value $0.01 per Common Share) $ 23.86
=============
Number of Common Shares outstanding (unlimited number of Common Shares has been authorized)... 17,550,236
=============

See Notes to Financial Statements Page 9

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENT OF OPERATIONS
FOR THE SIX MONTHS ENDED MAY 31, 2013 (UNAUDITED)

INVESTMENT INCOME:

Dividends (net of foreign withholding tax of $225,521)......................................... $ 5,855,309
Interest....................................................................................... 3,333
-------------
Total investment income..................................................................... 5,858,642
-------------
EXPENSES:
Investment advisory fees....................................................................... 2,788,593
Interest and fees on loan...................................................................... 602,607
Administrative fees............................................................................ 228,408
Printing fees.................................................................................. 54,467
Audit and tax fees............................................................................. 25,664
Custodian fees................................................................................. 22,594
Legal fees..................................................................................... 20,673
Trustees' fees and expenses.................................................................... 16,663
Transfer agent fees............................................................................ 14,026
Financial reporting fees....................................................................... 4,625
Other.......................................................................................... 24,480
-------------
Total expenses.............................................................................. 3,802,800
-------------
NET INVESTMENT INCOME (LOSS)................................................................... 2,055,842
-------------
NET REALIZED AND UNREALIZED GAIN (LOSS):
Net realized gain (loss) on:
Investments................................................................................. 33,708,351
Written options (a)......................................................................... 1,308,839
Foreign currency transactions............................................................... (34,592)
Swap contracts.............................................................................. 426,207
-------------
Net realized gain (loss)....................................................................... 35,408,805
-------------
Net change in unrealized appreciation (depreciation) on:
Investments................................................................................. 14,056,636
Written options (a)......................................................................... (782,331)
Foreign currency translation................................................................ (2,533)
Swap contracts.............................................................................. (587,712)
-------------
Net change in unrealized appreciation (depreciation)........................................... 12,684,060
-------------
NET REALIZED AND UNREALIZED GAIN (LOSS)........................................................ 48,092,865
-------------
NET INCREASE (DECREASE) IN NET ASSETS RESULTING FROM OPERATIONS................................ $ 50,148,707
=============

---------------------------------------

(a) Primary risk exposure is equity option contracts.

Page 10 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENTS OF CHANGES IN NET ASSETS

SIX MONTHS
ENDED PERIOD
5/31/2013 ENDED
(UNAUDITED) 11/30/2012
-------------- --------------
OPERATIONS:

Net investment income (loss)....................................................... $ 2,055,842 $ 4,785,848
Net realized gain (loss)........................................................... 35,408,805 36,621,810
Net increase from payment by the Sub-Advisor....................................... -- 104
Net change in unrealized appreciation (depreciation)............................... 12,684,060 5,198,386
------------ ------------
Net increase (decrease) in net assets resulting from operations.................... 50,148,707 46,606,148
------------ ------------
DISTRIBUTIONS TO SHAREHOLDERS FROM:
Net investment income.............................................................. (7,722,104) (5,424,795)
Net realized gain.................................................................. (22,841,632) (17,425,612)
Return of capital.................................................................. -- --
------------ ------------
Total distributions to shareholders................................................ (30,563,736) (22,850,407)
------------ ------------
CAPITAL TRANSACTIONS:
Offering costs..................................................................... -- 103,795
------------ ------------
Net increase (decrease) in net assets resulting from capital transactions.......... -- 103,795
------------ ------------
Total increase (decrease) in net assets............................................ 19,584,971 23,859,536

NET ASSETS:
Beginning of period................................................................ 399,091,735 375,232,199
------------ ------------
End of period...................................................................... $418,676,706 $399,091,735
============ ============
Accumulated net investment income (loss) at end of period.......................... $ (4,641,541) $ 1,024,721
============ ============
COMMON SHARES:
Common Shares at end of period..................................................... 17,550,236 17,550,236
============ ============

See Notes to Financial Statements Page 11

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENT OF CASH FLOWS
FOR THE SIX MONTHS ENDED MAY 31, 2013 (UNAUDITED)

CASH FLOWS FROM OPERATING ACTIVITIES:

Net increase (decrease) in net assets resulting from operations.................... $ 50,148,707
Adjustments to reconcile net increase (decrease) in net assets resulting from
operations to net cash provided by operating activities:
Purchases of investments........................................................ (216,814,071)
Sales of investments............................................................ 229,183,756
Proceeds from written options................................................... 2,389,906
Return of capital received from investment in MLPs.............................. 3,711,470
Net realized gain/loss on investments and options............................... (35,017,190)
Net change in unrealized appreciation/depreciation on investments and
options....................................................................... (13,274,305)
Net change in unrealized appreciation/depreciation on swap contracts ........... 587,712
Increase in cash segregated as collateral for open total return swaps .......... (2,700,000)

CHANGES IN ASSETS AND LIABILITIES:
Increase in interest receivable................................................. (567)
Decrease in dividends receivable (a)............................................ 588,522
Increase in prepaid expenses.................................................... (7,609)
Decrease in interest and fees on loan payable................................... (2,046)
Increase in investment advisory fees payable.................................... 64,660
Decrease in audit and tax fees payable.......................................... (18,336)
Increase in legal fees payable.................................................. 3,609
Decrease in printing fees payable............................................... (17,408)
Increase in administrative fees payable......................................... 7,015
Increase in custodian fees payable.............................................. 22,593
Decrease in transfer agent fees payable......................................... (1,357)
Increase in Trustees' fees and expenses payable................................. 456
Decrease in other liabilities................................................... (3,058)
-------------
CASH PROVIDED BY OPERATING ACTIVITIES.............................................. $ 18,852,459
-------------
CASH FLOWS FROM FINANCING ACTIVITIES:
Distributions to Common Shareholders from net realized gain................... (22,841,632)
Distributions to Common Shareholders from net investment income............... (7,722,104)
Proceeds from borrowing....................................................... 10,000,000
Repayment of borrowing........................................................ (6,000,000)
-------------
CASH USED IN FINANCING ACTIVITIES.................................................. (26,563,736)
-------------
Decrease in cash................................................................... (7,711,277)
Cash at beginning of period........................................................ 13,999,594
-------------
CASH AT END OF PERIOD.............................................................. $ 6,288,317
=============
SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
Cash paid during the period for interest and fees.................................. $ 604,653
=============

--------------------------------------------------------------------

(a) Includes net change in unrealized appreciation (depreciation) on foreign
currency of ($2,533).

Page 12 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
FINANCIAL HIGHLIGHTS
FOR A COMMON SHARE OUTSTANDING THROUGHOUT EACH PERIOD

SIX MONTHS
ENDED YEAR PERIOD
5/31/2013 ENDED ENDED
(UNAUDITED) 11/30/2012 11/30/2011 (a)
------------- ------------- -------------

Net asset value, beginning of period ................. $ 22.74 $ 21.38 $ 19.10 (b)
--------- --------- ---------
INCOME FROM INVESTMENT OPERATIONS:
Net investment income (loss) ......................... 0.12 0.27 0.05
Net realized and unrealized gain (loss) .............. 2.74 2.38 2.30
--------- --------- ---------
Total from investment operations ..................... 2.86 2.65 2.35
--------- --------- ---------
Common Shares offering costs charged to paid-in
capital ............................................ -- 0.01 (0.04)
--------- --------- ---------
Capital reduction from issuance of Common Shares
related to over allotment .......................... -- -- (0.03)
--------- --------- ---------
DISTRIBUTIONS PAID TO SHAREHOLDERS FROM:
Net investment income ................................ (0.44) (1.01) --
Net realized gain .................................... (1.30) (0.29) --
--------- --------- ---------
Total distributions to Common Shareholders ........... (1.74) (1.30) --
--------- --------- ---------
Net asset value, end of period ....................... $ 23.86 $ 22.74 $ 21.38
========= ========= =========
Market value, end of period .......................... $ 23.08 $ 21.34 $ 19.82
========= ========= =========
TOTAL RETURN BASED ON NET ASSET VALUE (c) ............ 13.24% 13.08% (d) 11.94%
========= ========= =========
TOTAL RETURN BASED ON MARKET VALUE (c) ............... 16.72% 14.47% (0.90)%
========= ========= =========
--------------------

RATIOS TO AVERAGE NET ASSETS/SUPPLEMENTAL DATA:
Net assets, end of period (in 000's) ................. $ 418,677 $ 399,092 $ 375,232
Ratio of total expenses to average net assets ........ 1.84% (e) 1.82% 1.66% (e)
Ratio of total expenses to average net assets
excluding interest expense and fees on loan ........ 1.55% (e) 1.52% 1.48% (e)
Ratio of net investment income (loss) to average net
assets ............................................. 0.99% (e) 1.21% 1.49% (e)
Portfolio turnover rate .............................. 40% 46% 8%

INDEBTEDNESS:
Total loan outstanding (in 000's) .................... $ 145,900 $ 141,900 $ 102,000
Asset coverage per $1,000 of indebtedness (f) ........ $ 3,870 $ 3,812 $ 4,679

--------------------

(a) Initial seed date of August 18, 2011. The Fund commenced operations on
September 27, 2011.

(b) Net of sales load of $0.90 per Common Share on initial offering.

(c) Total return is based on the combination of reinvested dividend, capital
gain and return of capital distributions, if any, at prices obtained by
the Dividend Reinvestment Plan, and changes in net asset value per share
for net asset value returns and changes in Common Share price for market
value returns. Total returns do not reflect sales load and are not
annualized for periods less than one year. Past performance is not
indicative of future results.

(d) The Fund received a reimbursement from the Sub-Advisor in the amount of
$104 in connection with a trade error. The reimbursement from the
Sub-Advisor represents less than $0.01 per share and had no effect on the
Fund's total return.

(e) Annualized.

(f) Calculated by taking the Fund's total assets less the Fund's total
liabilities (not including the loan outstanding) and dividing by the
outstanding loan balance in 000's.

See Notes to Financial Statements Page 13

--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

1. ORGANIZATION

First Trust Energy Infrastructure Fund (the "Fund") is a non-diversified,
closed-end management investment company organized as a Massachusetts business
trust on February 22, 2011, and is registered with the Securities and Exchange
Commission ("SEC") under the Investment Company Act of 1940, as amended (the
"1940 Act"). The Fund trades under the ticker symbol FIF on the New York Stock
Exchange ("NYSE").

The Fund's investment objective is to seek a high level of total return with an
emphasis on current distributions paid to shareholders. The Fund seeks to
achieve its objective by investing primarily in securities of companies engaged
in the energy infrastructure sector. Energy infrastructure companies principally
include publicly-traded master limited partnerships and limited liability
companies taxed as partnerships ("MLPs"), MLP affiliates, Canadian income trusts
and their successor companies (collectively, "Canadian Income Equities"),
pipeline companies, utilities, and other companies that derive at least 50% of
their revenues from operating or providing services in support of infrastructure
assets such as pipelines, power transmission and petroleum and natural gas
storage in the petroleum, natural gas and power generation industries
(collectively, "Energy Infrastructure Companies"). For purposes of the Fund's
investment objective, total return includes capital appreciation of, and all
distributions received from, securities in which the Fund will invest, taking
into account the varying tax characteristics of such securities. There can be no
assurance that the Fund will achieve its investment objective. The Fund may not
be appropriate for all investors.

2. SIGNIFICANT ACCOUNTING POLICIES

The following is a summary of significant accounting policies consistently
followed by the Fund in the preparation of its financial statements. The
preparation of financial statements in accordance with accounting principles
generally accepted in the United States of America ("U.S. GAAP") requires
management to make estimates and assumptions that affect the reported amounts
and disclosures in the financial statements. Actual results could differ from
those estimates.

A. PORTFOLIO VALUATION:

The net asset value ("NAV") of the Common Shares of the Fund is determined daily
as of the close of regular trading on the NYSE, normally 4:00 p.m. Eastern time,
on each day the NYSE is open for trading. If the NYSE closes early on a
valuation day, the NAV is determined as of that time. The NAV per Common Share
is calculated by dividing the value of all assets of the Fund (including accrued
interest and dividends), less all liabilities (including accrued expenses,
dividends declared but unpaid and any borrowings of the Fund) by the total
number of Common Shares outstanding.

The Fund's investments are valued daily in accordance with valuation procedures
adopted by the Fund's Board of Trustees, and in accordance with provisions of
the 1940 Act. The Fund's securities will be valued as follows:

Common stocks, MLPs and other equity securities listed on any national or
foreign exchange (excluding the NASDAQ(R) Stock Market, LLC ("NASDAQ") and
the London Stock Exchange Alternative Investment Market ("AIM")) are
valued at the last sale price on the exchange on which they are
principally traded or, for NASDAQ and AIM securities, the official closing
price. Securities traded on more than one securities exchange are valued
at the last sale price or official closing price, as applicable, at the
close of the securities exchange representing the principal market for
such securities.

Exchange-traded options and futures contracts are valued at the closing
price in the market where such contracts are principally traded. If no
closing price is available, exchange-traded options and futures contracts
are valued at the mean between the most recent bid and asked prices.
Over-the-counter options and futures contracts are valued at their closing
bid prices.

Swaps are valued utilizing quotations provided by a third party pricing
service.

Short-term investments that mature in less than 60 days when purchased are
valued at amortized cost.

All market quotations used in valuing the Fund's securities will be obtained
from a third party pricing service. If no quotation is received from a pricing
service, attempts will be made to obtain one or more broker quotes for the
security. In the event the pricing service does not provide a valuation, broker
quotations are not readily available, or the valuations received are deemed
unreliable, the Fund's Board of Trustees has designated First Trust Advisors
L.P. ("First Trust") to use a fair value method to value the Fund's securities.
Additionally, if events occur after the close of the principal markets for
certain securities (e.g., domestic debt and foreign securities) that could
materially affect the Fund's NAV, First Trust will use a fair value method to
value the Fund's securities. The use of fair value pricing is governed by
valuation procedures adopted by the Fund's Board of Trustees, and in accordance
with the provisions of the 1940 Act. As a general principle, the fair value of a
security is the amount which the Fund might reasonably expect to receive for the
security upon its current sale. In light of the judgment involved in fair
valuations, there can be no assurance that a fair value assigned to a particular
security will be the amount which the Fund might be able to receive upon its
current sale. Fair valuation of a security will be based on the consideration of
all available information, including, but not limited to, the following:

1) the type of security;

2) the size of the holding;

3) the initial cost of the security;

4) transactions in comparable securities;

5) price quotes from dealers and/or pricing services;

Page 14

--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

6) relationships among various securities;

7) information obtained by contacting the issuer, analysts, or the
appropriate stock exchange;

8) an analysis of the issuer's financial statements; and

9) the existence of merger proposals or tender offers that might affect
the value of the security.

If the securities in question are foreign securities, the following additional
information may be considered:

1) the value of similar foreign securities traded on other foreign
markets;

2) ADR trading of similar securities;

3) closed-end fund trading of similar securities;

4) foreign currency exchange activity;

5) the trading prices of financial products that are tied to baskets of
foreign securities;

6) factors relating to the event that precipitated the pricing problem;

7) whether the event is likely to recur; and

8) whether the effects of the event are isolated or whether they affect
entire markets, countries or regions.

The Fund is subject to fair value accounting standards that define fair value,
establish the framework for measuring fair value and provide a three-level
hierarchy for fair valuation based upon the inputs to the valuation as of the
measurement date. The three levels of the fair value hierarchy are as follows:

o Level 1 - Level 1 inputs are quoted prices in active markets for
identical investments. An active market is a market in which
transactions for the investment occur with sufficient frequency and
volume to provide pricing information on an ongoing basis.

o Level 2 - Level 2 inputs are observable inputs, either directly or
indirectly, and include the following:

o Quoted prices for similar investments in active markets.

o Quoted prices for identical or similar investments in markets
that are non-active. A non-active market is a market where
there are few transactions for the investment, the prices are
not current, or price quotations vary substantially either
over time or among market makers, or in which little
information is released publicly.

o Inputs other than quoted prices that are observable for the
investment (for example, interest rates and yield curves
observable at commonly quoted intervals, volatilities,
prepayment speeds, loss severities, credit risks, and default
rates).

o Inputs that are derived principally from or corroborated by
observable market data by correlation or other means.

o Level 3 - Level 3 inputs are unobservable inputs. Unobservable
inputs may reflect the reporting entity's own assumptions about the
assumptions that market participants would use in pricing the
investment.

The inputs or methodology used for valuing investments are not necessarily an
indication of the risk associated with investing in those investments. A summary
of the inputs used to value the Fund's investments as of May 31, 2013, is
included with the Fund's Portfolio of Investments.

B. OPTION CONTRACTS:

The Fund is subject to equity price risk in the normal course of pursuing its
investment objective and may write (sell) options to hedge against changes in
the value of equities. Also, the Fund seeks to generate additional income, in
the form of premiums received, from writing (selling) the options. The Fund may
write (sell) covered call or put options ("options") on all or a portion of the
common stock of energy companies held in the Fund's portfolio as determined to
be appropriate by Energy Income Partners, LLC ("EIP" or the "Sub-Advisor"). The
number of options the Fund can write (sell) is limited by the amount of common
stock of energy companies the Fund holds in its portfolio. The Fund will not
write (sell) "naked" or uncovered options. When the Fund writes (sells) an
option, an amount equal to the premium received by the Fund is included in
"Options written, at value" on the Fund's Statement of Assets and Liabilities.
Options are marked-to-market daily and their value will be affected by changes
in the value and dividend rates of the underlying equity securities, changes in
interest rates, changes in the actual or perceived volatility of the securities
markets and the underlying equity securities and the remaining time to the
options' expiration. The value of options may also be adversely affected if the
market for the options becomes less liquid or trading volume diminishes.

Options the Fund writes (sells) will either be exercised, expire or be cancelled
pursuant to a closing transaction. If the price of the underlying equity
security exceeds the option's exercise price, it is likely that the option
holder will exercise the option. If an option written (sold) by the Fund is
exercised, the Fund would be obligated to deliver the underlying equity security
to the option holder upon payment of the strike price. In this case, the option
premium received by the Fund will be added to the amount realized on the sale of
the underlying security for purposes of determining gain or loss. If the price
of the underlying equity security is less than the option's strike price, the
option will likely expire without being exercised. The option premium received
by the Fund will, in this case, be treated as short-term capital gain on the
expiration date of the option. The Fund may also elect to close out its position
in an option prior to its expiration by purchasing an option of the same series
as the option written (sold) by the Fund. Gain or loss on options is presented
separately as "Net realized gain (loss) on written options" on the Statement of
Operations.

The options that the Fund writes (sells) give the option holder the right, but
not the obligation, to purchase a security from the Fund at the strike price on
or prior to the option's expiration date. The ability to successfully implement
the writing (selling) of covered call options depends on the ability of the
Sub-Advisor to predict pertinent market movements, which cannot be assured.
Thus, the use of options may

Page 15

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

require the Fund to sell portfolio securities at inopportune times or for prices
other than current market value, which may limit the amount of appreciation the
Fund can realize on an investment, or may cause the Fund to hold a security that
it might otherwise sell. As the writer (seller) of a covered option, the Fund
foregoes, during the option's life, the opportunity to profit from increases in
the market value of the security covering the option above the sum of the
premium and the strike price of the option, but has retained the risk of loss
should the price of the underlying security decline. The writer (seller) of an
option has no control over the time when it may be required to fulfill its
obligation as a writer (seller) of the option. Once an option writer (seller)
has received an exercise notice, it cannot effect a closing purchase transaction
in order to terminate its obligation under the option and must deliver the
underlying security to the option holder at the exercise price.

Over-the-counter options have the risk of the potential inability of
counterparties to meet the terms of their contracts. The Fund's maximum equity
price risk for purchased options is limited to the premium initially paid. In
addition, certain risks may arise upon entering into option contracts including
the risk that an illiquid secondary market will limit the Fund's ability to
close out an option contract prior to the expiration date and that a change in
the value of the option contract may not correlate exactly with changes in the
value of the securities hedged.

C. SWAP AGREEMENTS

The Fund may enter into swap agreements as a substitute for investing in certain
securities. A swap is a financial instrument that typically involves the
exchange of cash flows between two parties ("Counterparties") on specified dates
(settlement dates) where the cash flows are based on agreed-upon prices, rates,
etc. In a typical swap agreement, one party agrees to pay another party the
return on a security or basket of securities in return for payment of a
specified interest rate. By entering into swaps, the Fund can gain exposure to a
security without actually purchasing the underlying asset. Swap agreements
involve the risk associated with the investment in the security as well as the
risk that the performance of the security, including any dividends, will not
exceed the interest that the Fund will be committed to pay under the swap. Swap
agreements are individually negotiated and involve the risk of the potential
inability of the Counterparties to meet the terms of the agreement. In
connection with these agreements, cash and securities may be identified as
collateral in accordance with the terms of the respective swap agreements to
provide assets of value and recourse in the event of default under the swap
agreement or bankruptcy/insolvency of a party to the swap agreement. In the
event of a default by the Counterparty, the Fund will seek withdrawal of this
collateral and may incur certain costs exercising its right with respect to the
collateral. If a Counterparty becomes bankrupt or otherwise fails to perform its
obligations due to financial difficulties, the Fund may experience significant
delays in obtaining any recovery in a bankruptcy or other reorganization
proceeding. The Fund may obtain only limited recovery or may obtain no recovery
in such circumstances. Swap agreements may increase or decrease the overall
volatility of the investments of the Fund. The performance of swap agreements
may be affected by a change in the specific interest rate, security, currency,
or other factors that determine the amounts of payments due to and from the
Fund. A total return equity swap agreement would expose the Fund to the same
equity price risk as it would have if the underlying equity securities were
purchased. The Fund's maximum equity price risk to meet its future payments
under swap agreements outstanding as of May 31, 2013, is equal to the total
notional amount as shown on the Portfolio of Investments. The notional amount
represents the U.S. dollar value of the contract as of the day of the opening
transaction or contract reset. The Fund entered into a Total Return Equity Swap
agreement on January 22, 2013. The average volume of Total Return Equity Swaps
was $6,770,563 for the period January 22, 2013, to May 31, 2013.

D. SECURITIES TRANSACTIONS AND INVESTMENT INCOME:

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.
Dividend income is recorded on the ex-dividend date. Interest income is recorded
daily on the accrual basis, including amortization of premiums and accretion of
discounts. The Fund will rely to some extent on information provided by the
MLPs, which is not necessarily timely, to estimate taxable income allocable to
the MLP units held in the Fund's portfolio.

Distributions received from the Fund's investments in MLPs generally are
comprised of return of capital and investment income. The Fund records estimated
return of capital and investment income based on historical information
available from each MLP. These estimates may subsequently be revised based on
information received from the MLPs after their tax reporting periods are
concluded. For the six months ended May 31, 2013, distributions of $3,711,470
received from MLPs have been reclassified as return of capital.

E. DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS:

The Fund will distribute to holders of its Common Shares monthly dividends of
all or a portion of its net income after the payment of interest in connection
with leverage, if any. Distributions of any long-term capital gains earned by
the Fund are distributed at least annually. Distributions will automatically be
reinvested into additional Common Shares pursuant to the Fund's Dividend
Reinvestment Plan unless cash distributions are elected by the shareholder.

Distributions from income and capital gains are determined in accordance with
income tax regulations, which may differ from U.S. GAAP. Certain capital
accounts in the financial statements are periodically adjusted for permanent
differences in order to reflect their tax character. These permanent differences
are primarily due to the varying treatment of income and gain/loss on portfolio
securities held by the Fund and have no impact on net assets or NAV per share.
Temporary differences, which arise from recognizing certain items of income,
expense and gain/loss in different periods for financial statement and tax
purposes, will reverse at some point in the future.

Page 16

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

The tax character of distributions paid during the fiscal year ended November
30, 2012, was as follows:

Distributions paid from:
Ordinary income................................... $ 22,850,407

As of November 30, 2012, the components of distributable earnings and net assets
on a tax basis were as follows:

Undistributed ordinary income..................... $ 21,712,858
Undistributed capital gains....................... 1,606,644
-------------
Total undistributed earnings...................... 23,319,502
Accumulated capital and other losses.............. --
Net unrealized appreciation (depreciation)........ 40,467,156
-------------
Total accumulated earnings (losses)............... 63,786,658
Other .......................................... 683,251
Paid-in capital................................... 334,621,826
-------------
Net assets........................................ $ 399,091,735
=============

F. INCOME TAXES:

The Fund intends to continue to qualify as a regulated investment company by
complying with the requirements under Subchapter M of the Internal Revenue Code
of 1986, as amended, which includes distributing substantially all of its net
investment income and net realized gains to shareholders. Accordingly, no
provision has been made for federal or state income taxes. However, due to the
timing and amount of distributions, the Fund may be subject to an excise tax of
4% of the amount by which approximately 98% of the Fund's taxable income exceeds
the distributions from such taxable income for the calendar year.

At November 30, 2012, the Fund had no capital loss carryforward for federal
income tax purposes.

The Fund is subject to accounting standards that establish a minimum threshold
for recognizing, and a system for measuring, the benefits of a tax position
taken or expected to be taken in a tax return. Taxable years ending 2011 and
2012 remain open to federal and state audit. As of November 30, 2012, management
has evaluated the application of these standards to the Fund and has determined
that no provision for income tax is required in the Fund's financial statements
for uncertain tax positions.

G. EXPENSES:

The Fund will pay all expenses directly related to its operations.

H. FOREIGN CURRENCY:

The books and records of the Fund are maintained in U.S. dollars. Foreign
currencies, investments and other assets and liabilities are translated into
U.S. dollars at the exchange rates prevailing at the end of the period.
Purchases and sales of investment securities and items of income and expense are
translated on the respective dates of such transactions. Unrealized gains and
losses on assets and liabilities, other than investments in securities, which
result from changes in foreign currency exchange rates have been included in
"Net change in unrealized appreciation (depreciation) on foreign currency
translation" on the Statement of Operations. Unrealized gains and losses on
investments in securities which result from changes in foreign exchange rates
are included with fluctuations arising from changes in market price and are
shown in "Net change in unrealized appreciation (depreciation) on investments"
on the Statement of Operations. Net realized foreign currency gains and losses
include the effect of changes in exchange rates between trade date and
settlement date on investment security transactions, foreign currency
transactions and interest and dividends received. The portion of foreign
currency gains and losses related to fluctuation in exchange rates between the
initial purchase trade date and subsequent sale trade date is included in "Net
realized gain (loss) on foreign currency transactions" on the Statement of
Operations.

I. ORGANIZATION AND OFFERING COSTS:

Organization costs consisted of costs incurred to establish the Fund and enable
it to legally conduct business. These costs included filing fees, listing fees,
legal services pertaining to the organization of the business and audit fees
relating to the initial registration and auditing the initial statement of
assets and liabilities, among other fees. Offering costs consisted of legal fees
pertaining to the Fund's shares offered for sale, registration fees,
underwriting fees, and printing of the initial prospectus, among other fees.
First Trust paid all organization expenses. The Fund's Common Share offering
costs of $690,000 were recorded as a reduction of the proceeds from the sale of
Common Shares during the period ended November 30, 2011. During the fiscal year
ended November 30, 2012, it was determined that actual offering costs were less
than the estimated offering costs by $103,795. Therefore, paid-in capital was
increased by that amount during the fiscal year ended November 30, 2012, as
reflected in the offering costs line item on the Statements of Changes in Net
Assets.

Page 17

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

3. INVESTMENT ADVISORY FEE, AFFILIATED TRANSACTIONS AND OTHER FEE ARRANGEMENTS

First Trust, the investment advisor to the Fund, is a limited partnership with
one limited partner, Grace Partners of DuPage L.P., and one general partner, The
Charger Corporation. The Charger Corporation is an Illinois corporation
controlled by James A. Bowen, Chief Executive Officer of First Trust. First
Trust is responsible for the ongoing monitoring of the Fund's investment
portfolio, managing the Fund's business affairs and providing certain
administrative services necessary for the management of the Fund. For these
investment management services, First Trust is entitled to a monthly fee
calculated at an annual rate of 1.00% of the Fund's Managed Assets. First Trust
also provides fund reporting services to the Fund for a flat annual fee in the
amount of $9,250.

EIP serves as the Fund's sub-advisor and manages the Fund's portfolio subject to
First Trust's supervision. The Sub-Advisor receives a monthly sub-advisory fee
calculated at an annual rate of 0.50% of the Fund's Managed Assets that is paid
by First Trust out of its investment advisory fee.

First Trust Capital Partners, LLC ("FTCP"), an affiliate of First Trust, owns,
through a wholly-owned subsidiary, a 15% ownership interest in each of the
Sub-Advisor and EIP Partners, LLC, an affiliate of the Sub-Advisor. In addition,
as of November 29, 2012, FTCP, through a wholly-owned subsidiary, purchased a
preferred interest in the Sub-Advisor. The preferred interest is non-voting and
does not share in the profits or losses of the Sub-Advisor. The Sub-Advisor may
buy back any or all of FTCP's preferred interest at any time and FTCP may sell
back to the Sub-Advisor up to 50% of its preferred interest on or after July 29,
2014, and any or all of its preferred interest after November 29, 2015.

BNY Mellon Investment Servicing (US) Inc. ("BNYM IS") serves as the Fund's
administrator, fund accountant and transfer agent in accordance with certain fee
arrangements. As administrator and fund accountant, BNYM IS is responsible for
providing certain administrative and accounting services to the Fund, including
maintaining the Fund's books of account, records of the Fund's securities
transactions, and certain other books and records. As transfer agent, BNYM IS is
responsible for maintaining shareholder records for the Fund. The Bank of New
York Mellon ("BNYM") serves as the Fund's custodian in accordance with certain
fee arrangements. As custodian, BNYM is responsible for custody of the Fund's
assets.

Each Trustee who is not an officer or employee of First Trust, any sub-advisor
or any of their affiliates ("Independent Trustees") is paid a fixed annual
retainer of $125,000 per year and an annual per fund fee of $4,000 for each
closed-end fund or other actively managed fund and $1,000 for each index fund in
the First Trust Fund Complex. The fixed annual retainer is allocated pro rata
among each fund in the First Trust Fund Complex based on net assets.

Additionally, the Lead Independent Trustee is paid $15,000 annually, the
Chairman of the Audit Committee is paid $10,000 annually, and each of the
Chairmen of the Nominating and Governance Committee and the Valuation Committee
is paid $5,000 annually to serve in such capacities, with such compensation
allocated pro rata among each fund in the First Trust Fund Complex based on net
assets. Trustees are reimbursed for travel and out-of-pocket expenses in
connection with all meetings. The Lead Independent Trustee and each Committee
Chairman will serve two-year terms until December 31, 2013, before rotating to
serve as Chairman of another Committee or as Lead Independent Trustee. After
December 31, 2013, the Lead Independent Trustee and Committee Chairmen will
rotate every three years. The officers and "Interested" Trustee receive no
compensation from the funds for acting in such capacities.

4. PURCHASES AND SALES OF SECURITIES

Cost of purchases and proceeds from sales of investments, excluding short-term
investments, for the six months ended May 31, 2013, were $216,511,630 and
$227,307,258, respectively.

Written option activity for the Fund was as follows:

NUMBER
OF
WRITTEN OPTIONS CONTRACTS PREMIUMS
--------------------------------------------------------------------------------
Options outstanding at November 30, 2012.......... 35,234 $ 1,576,846
Options Written................................... 54,218 2,389,906
Options Expired................................... (27,474) (1,308,839)
Options Exercised................................. (25,317) (1,121,902)
Options Closed.................................... -- --
--------- ------------
Options outstanding at May 31, 2013............... 36,661 $ 1,536,011
========= ============

5. BORROWINGS

The Fund has a committed facility agreement with The Bank of Nova Scotia
("Scotia") that has a maximum commitment amount of $165,000,000. The borrowing
rate under the facility is equal to the 1-month LIBOR plus 65 basis points. In
addition, under the facility, the Fund pays a commitment fee of 0.20% on the
undrawn amount of such facility. The average amount outstanding for the six
months ended

Page 18

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

May 31, 2013, was $143,954,945 with a weighted average interest rate of 0.81%.
As of May 31, 2013, the Fund had outstanding borrowings of $145,900,000 under
this committed facility agreement. The high and low annual interest rates for
the six months ended May 31, 2013, were 0.87% and 0.79%, respectively. The
interest rate at May 31, 2013, was 0.79%.

6. INDEMNIFICATION

The Fund has a variety of indemnification obligations under contracts with its
service providers. The Fund's maximum exposure under these arrangements is
unknown. However, the Fund has not had prior claims or losses pursuant to these
contracts and expects the risk of loss to be remote.

7. INDUSTRY CONCENTRATION RISK

The Fund invests at least 80% of its Managed Assets in securities issued by
Energy Infrastructure Companies. Given this industry concentration, the Fund is
more susceptible to adverse economic or regulatory occurrences affecting that
industry than an investment company that is not concentrated in a single
industry. Energy Infrastructure Company issuers may be subject to a variety of
factors that may adversely affect their business or operations, including high
interest costs in connection with capital construction programs, high leverage
costs associated with environmental and other regulations, the effects of
economic slowdown, surplus capacity, increased competition from other providers
of services, uncertainties concerning the availability of fuel at reasonable
prices, the effects of energy conservation policies and other factors.

8. SUBSEQUENT EVENTS

Management has evaluated the impact of all subsequent events to the Fund through
the date the financial statements were issued, and has determined that there
were the following subsequent events:

On June 20, 2013, the Fund declared a dividend of $0.11 per share to Common
Shareholders of record on July 3, 2013, payable July 15, 2013.

On July 22, 2013, the Fund declared a dividend of $0.11 per share to Common
Shareholders of record on August 5, 2013, payable August 15, 2013.

Page 19

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ADDITIONAL INFORMATION
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

DIVIDEND REINVESTMENT PLAN

If your Common Shares are registered directly with the Fund or if you hold your
Common Shares with a brokerage firm that participates in the Fund's Dividend
Reinvestment Plan (the "Plan"), unless you elect, by written notice to the Fund,
to receive cash distributions, all dividends, including any capital gain
distributions, on your Common Shares will be automatically reinvested by BNY
Mellon Investment Servicing (US) Inc. (the "Plan Agent"), in additional Common
Shares under the Plan. If you elect to receive cash distributions, you will
receive all distributions in cash paid by check mailed directly to you by the
Plan Agent, as the dividend paying agent.

If you decide to participate in the Plan, the number of Common Shares you will
receive will be determined as follows:

(1) If Common Shares are trading at or above net asset value ("NAV") at
the time of valuation, the Fund will issue new shares at a price
equal to the greater of (i) NAV per Common Share on that date or
(ii) 95% of the market price on that date.

(2) If Common Shares are trading below NAV at the time of valuation, the
Plan Agent will receive the dividend or distribution in cash and
will purchase Common Shares in the open market, on the NYSE or
elsewhere, for the participants' accounts. It is possible that the
market price for the Common Shares may increase before the Plan
Agent has completed its purchases. Therefore, the average purchase
price per share paid by the Plan Agent may exceed the market price
at the time of valuation, resulting in the purchase of fewer shares
than if the dividend or distribution had been paid in Common Shares
issued by the Fund. The Plan Agent will use all dividends and
distributions received in cash to purchase Common Shares in the open
market within 30 days of the valuation date except where temporary
curtailment or suspension of purchases is necessary to comply with
federal securities laws. Interest will not be paid on any uninvested
cash payments.

You may elect to opt-out of or withdraw from the Plan at any time by giving
written notice to the Plan Agent, or by telephone at (866) 340-1104, in
accordance with such reasonable requirements as the Plan Agent and the Fund may
agree upon. If you withdraw or the Plan is terminated, you will receive a
certificate for each whole share in your account under the Plan, and you will
receive a cash payment for any fraction of a share in your account. If you wish,
the Plan Agent will sell your shares and send you the proceeds, minus brokerage
commissions.

The Plan Agent maintains all Common Shareholders' accounts in the Plan and gives
written confirmation of all transactions in the accounts, including information
you may need for tax records. Common Shares in your account will be held by the
Plan Agent in non-certificated form. The Plan Agent will forward to each
participant any proxy solicitation material and will vote any shares so held
only in accordance with proxies returned to the Fund. Any proxy you receive will
include all Common Shares you have received under the Plan.

There is no brokerage charge for reinvestment of your dividends or distributions
in Common Shares. However, all participants will pay a pro rata share of
brokerage commissions incurred by the Plan Agent when it makes open market
purchases.

Automatically reinvesting dividends and distributions does not mean that you do
not have to pay income taxes due upon receiving dividends and distributions.
Capital gains and income are realized although cash is not received by you.
Consult your financial advisor for more information.

If you hold your Common Shares with a brokerage firm that does not participate
in the Plan, you will not be able to participate in the Plan and any dividend
reinvestment may be effected on different terms than those described above.

The Fund reserves the right to amend or terminate the Plan if in the judgment of
the Board of Trustees the change is warranted. There is no direct service charge
to participants in the Plan; however, the Fund reserves the right to amend the
Plan to include a service charge payable by the participants. Additional
information about the Plan may be obtained by writing BNY Mellon Investment
Servicing (US) Inc., 301 Bellevue Parkway, Wilmington, Delaware 19809.

PROXY VOTING POLICIES AND PROCEDURES

A description of the policies and procedures that the Fund uses to determine how
to vote proxies and information on how the Fund voted proxies relating to
portfolio investments during the most recent 12-month period ended June 30 is
available (1) without charge, upon request, by calling (800) 988-5891; (2) on
the Fund's website located at http://www.ftportfolios.com; and (3) on the
Securities and Exchange Commission's ("SEC") website located at
http://www.sec.gov.

Page 20

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ADDITIONAL INFORMATION (CONTINUED)
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

PORTFOLIO HOLDINGS

The Fund files its complete schedule of portfolio holdings with the SEC for the
first and third quarters of each fiscal year on Form N-Q. The Fund's Forms N-Q
are available (1) by calling (800) 988-5891; (2) on the Fund's website located
at http://www.ftportfolios.com; (3) on the SEC's website at http://www.sec.gov;
and (4) for review and copying at the SEC's Public Reference Room ("PRR") in
Washington, DC. Information regarding the operation of the PRR may be obtained
by calling (800) SEC-0330.

SUBMISSION OF MATTERS TO A VOTE OF SHAREHOLDERS

The Joint Annual Meeting of Shareholders of the Common Shares of First Trust
Energy Income and Growth Fund, First Trust Enhanced Equity Income Fund, First
Trust/Aberdeen Global Opportunity Income Fund, First Trust Mortgage Income Fund,
First Trust Strategic High Income Fund II, First Trust/Aberdeen Emerging
Opportunity Fund, First Trust Specialty Finance and Financial Opportunities
Fund, First Trust Active Dividend Income Fund, First Trust Energy Infrastructure
Fund, Macquarie/First Trust Global Infrastructure/Utilities Dividend & Income
Fund and First Trust High Income Long/Short Fund was held on April 17, 2013 (the
"Annual Meeting"). At the Annual Meeting, James A. Bowen and Niel B. Nielson
were elected by the Common Shareholders of the First Trust Energy Infrastructure
Fund as Class III Trustees for a three-year term expiring at the Fund's annual
meeting of shareholders in 2016. The number of votes cast in favor of Mr. Bowen
was 15,612,801, the number of votes against was 221,307 and the number of
abstentions was 1,716,128. The number of votes cast in favor of Mr. Nielson was
15,615,777, the number of votes against was 218,331 and the number of
abstentions was 1,716,128. Richard E. Erickson, Thomas R. Kadlec and Robert F.
Keith are the other current and continuing Trustees.

RISK CONSIDERATIONS

Risks are inherent in all investing. The following summarizes some, but not all,
of the risks that should be considered for the Fund. For additional information
about the risks associated with investing in the Fund, please see the Fund's
prospectus and statement of additional information, as well as other Fund
regulatory filings.

CURRENCY RISK: The value of securities denominated or quoted in foreign
currencies may be adversely affected by fluctuations in the relative currency
exchange rates and by exchange control regulations. The Fund's investment
performance may be negatively affected by a devaluation of a currency in which
the Fund's investments are denominated or quoted. Further, the Fund's investment
performance may be significantly affected, either positively or negatively, by
currency exchange rates because the U.S. dollar value of securities denominated
or quoted in another currency will increase or decrease in response to changes
in the value of such currency in relation to the U.S. dollar. While certain of
the Fund's non-U.S. dollar-denominated securities may be hedged into U.S.
dollars, hedging may not alleviate all currency risks.

INVESTMENT AND MARKET RISK: An investment in the Fund's Common Shares is subject
to investment risk, including the possible loss of the entire principal
invested. An investment in Common Shares represents an indirect investment in
the securities owned by the Fund. The value of these securities, like other
market investments, may move up or down, sometimes rapidly and unpredictably.
Common Shares at any point in time may be worth less than the original
investment, even after taking into account the reinvestment of Fund dividends
and distributions. Security prices can fluctuate for several reasons including
the general condition of the securities markets, or when political or economic
events affecting the issuers occur. When the Advisor or Sub-Advisor determines
that it is temporarily unable to follow the Fund's investment strategy or that
it is impractical to do so (such as when a market disruption event has occurred
and trading in the securities is extremely limited or absent), the Fund may take
temporary defensive positions.

LEVERAGE RISK: The use of leverage results in additional risks and can magnify
the effect of any losses. The funds borrowed pursuant to a leverage borrowing
program constitute a substantial lien and burden by reason of their prior claim
against the income of the Fund and against the net assets of the Fund in
liquidation. If the Fund is not in compliance with certain credit facility
provisions, the Fund may not be permitted to declare dividends or other
distributions.

MLP RISK: An investment in MLP units involves risks which differ from an
investment in common stock of a corporation. Holders of MLP units have limited
control and voting rights on matters affecting the partnership. In addition,
there are certain tax risks associated with an investment in MLP units and
conflicts of interest exist between common unit holders and the general partner,
including those arising from incentive distribution payments.

NON-U.S. RISK: The Fund may invest a portion of its assets in the equity
securities of issuers domiciled in jurisdictions other than the U.S. Investments
in the securities and instruments of non-U.S. issuers involve certain
considerations and risks not ordinarily associated with investments in
securities and instruments of U.S. issuers. Non-U.S. companies are not generally
subject to uniform accounting, auditing and financial standards and requirements
comparable to those applicable to U.S. companies. Non-U.S. securities exchanges,
brokers and listed

Page 21

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ADDITIONAL INFORMATION (CONTINUED)
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
MAY 31, 2013 (UNAUDITED)

companies may be subject to less government supervision and regulation than
exists in the United States. Dividend and interest income may be subject to
withholding and other non-U.S. taxes, which may adversely affect the net return
on such investments. A related risk is that there may be difficulty in obtaining
or enforcing a court judgment abroad.

QUALIFIED DIVIDEND INCOME TAX RISK: There can be no assurance as to what portion
of the distributions paid to the Fund's Common Shareholders will consist of
tax-advantaged qualified dividend income. Certain distributions designated by
the Fund as derived from qualified dividend income will be taxed in the hands of
non-corporate Common Shareholders at the rates applicable to long-term capital
gains, provided certain holding period and other requirements are satisfied by
both the Fund and the Common Shareholders. Additional requirements apply in
determining whether distributions by foreign issuers should be regarded as
qualified dividend income. Certain investment strategies of the Fund will limit
the Fund's ability to meet these requirements and consequently will limit the
amount of qualified dividend income received and distributed by the Fund. A
change in the favorable provisions of the federal tax laws with respect to
qualified dividends may result in a widespread reduction in announced dividends
and may adversely impact the valuation of the shares of dividend-paying
companies.

RESTRICTED SECURITIES RISK: The Fund may invest in unregistered or otherwise
restricted securities. The term "restricted securities" refers to securities
that are unregistered or are held by control persons of the issuer and
securities that are subject to contractual restrictions on their resale. As a
result, restricted securities may be more difficult to value and the Fund may
have difficulty disposing of such assets either in a timely manner or for a
reasonable price. In order to dispose of an unregistered security, the Fund,
where it has contractual rights to do so, may have to cause such security to be
registered. A considerable period may elapse between the time the decision is
made to sell the security and the time the security is registered so that the
Fund could sell it. Contractual restrictions on the resale of securities vary in
length and scope and are generally the result of a negotiation between the
issuer and acquirer of the securities. The Fund would, in either case, bear
market risks during that period.

Page 22

This Page Left Blank Intentionally.

FIRST TRUST

INVESTMENT ADVISOR
First Trust Advisors L.P.
120 E. Liberty Drive, Suite 400
Wheaton, IL 60187

INVESTMENT SUB-ADVISOR
Energy Income Partners, LLC
49 Riverside Avenue
Westport, CT 06880

ADMINISTRATOR,
FUND ACCOUNTANT &
TRANSFER AGENT
BNY Mellon Investment Servicing (US) Inc.
301 Bellevue Parkway
Wilmington, DE 19809

CUSTODIAN
The Bank of New York Mellon
101 Barclay Street, 20th Floor
New York, NY 10286

INDEPENDENT REGISTERED
PUBLIC ACCOUNTING FIRM
Deloitte & Touche LLP
111 S. Wacker Drive
Chicago, IL 60606

LEGAL COUNSEL
Chapman and Cutler LLP
111 W. Monroe Street
Chicago, IL 60603

[BLANK BACK COVER]

ITEM 2. CODE OF ETHICS.

Not applicable.

ITEM 3. AUDIT COMMITTEE FINANCIAL EXPERT.

Not applicable.

ITEM 4. PRINCIPAL ACCOUNTANT FEES AND SERVICES.

Not applicable.

ITEM 5. AUDIT COMMITTEE OF LISTED REGISTRANTS.

Not applicable.

ITEM 6. INVESTMENTS.

(a) Schedule of Investments in securities of unaffiliated issuers as of the
close of the reporting period is included as part of the report to
shareholders filed under Item 1 of this form.

(b) Not applicable.

ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END
MANAGEMENT INVESTMENT COMPANIES.

Not applicable.

ITEM 8. PORTFOLIO MANAGERS OF CLOSED-END MANAGEMENT INVESTMENT COMPANIES.

(a) Not applicable.

(b) There has been no change, as of the date of this filing, in any of the
portfolio managers identified in response to paragraph (a)(1) of this Item
in the registrant's most recently filed annual report on Form N-CSR.

ITEM 9. PURCHASES OF EQUITY SECURITIES BY CLOSED-END MANAGEMENT INVESTMENT
COMPANY AND AFFILIATED PURCHASERS.

Not applicable.

ITEM 10. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

There have been no material changes to the procedures by which the shareholders
may recommend nominees to the Registrant's board of trustees, where those
changes were implemented after the Registrant last provided disclosure in
response to the requirements of Item 407(c)(2)(iv) of Regulation S-K (17 CFR
229.407) (as required by Item 22(b)(15) of Schedule 14A (17 CFR 240.14a-101)),
or this Item.

ITEM 11. CONTROLS AND PROCEDURES.

(a) The Registrant's principal executive and principal financial officers, or
persons performing similar functions, have concluded that the
Registrant's disclosure controls and procedures (as defined in Rule
30a-3(c) under the Investment Company Act of 1940, as amended (the "1940
Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days
of the filing date of the report that includes the disclosure required by
this paragraph, based on their evaluation of these controls and
procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR
270.30a-3(b)) and Rules 13a-15(b) or 15d-15(b) under the Securities
Exchange Act of 1934, as amended (17 CFR 240.13a-15(b) or 240.15d-15(b)).

(b) There were no changes in the Registrant's internal control over financial
reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR
270.30a-3(d)) that occurred during the Registrant's second fiscal quarter
of the period covered by this report that has materially affected, or is
reasonably likely to materially affect, the Registrant's internal control
over financial reporting.

ITEM 12. EXHIBITS.

(a)(1) Not applicable.

(a)(2) Certifications pursuant to Rule 30a-2(a) under the 1940 Act and
Section 302 of the Sarbanes-Oxley Act of 2002 are attached hereto.

(a)(3) Not applicable.

(b) Certifications pursuant to Rule 30a-2(b) under the 1940 Act and Section
906 of the Sarbanes- Oxley Act of 2002 are attached hereto.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(registrant) First Trust Energy Infrastructure Fund
----------------------------------------------------------------

By (Signature and Title)* /s/ Mark R. Bradley
------------------------------------------------
Mark R. Bradley, President and
Chief Executive Officer
(principal executive officer)

Date July 23, 2013
---------------------

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By (Signature and Title)* /s/ Mark R. Bradley
------------------------------------------------
Mark R. Bradley, President and
Chief Executive Officer
(principal executive officer)

Date July 23, 2013
---------------------

By (Signature and Title)* /s/ James M. Dykas
------------------------------------------------
James M. Dykas, Treasurer, Chief Financial
Officer and Chief Accounting Officer
(principal financial officer)

Date July 23, 2013
---------------------

* Print the name and title of each signing officer under his or her signature.