UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED
MANAGEMENT INVESTMENT COMPANIES

ITEM 1. REPORT TO STOCKHOLDERS.

The Annual Report to Stockholders is filed herewith.

Annual Report  May 31, 2013

WESTERN ASSET

GLOBAL HIGH INCOME FUND INC. (EHI)

Fund objectives

The Fund’s primary investment objective is high current income. The Fund’s secondary investment objective is total return.

What’s inside

Dear Shareholder,

We are pleased to provide the annual report of Western Asset Global High Income Fund Inc. for the twelve-month reporting period ended May 31, 2013. Please read on for a detailed look at prevailing economic and market conditions during the Fund’s reporting period and to learn how those conditions have affected Fund performance.

I am pleased to introduce myself as the new Chairman, President and Chief Executive Officer of the Fund, succeeding R. Jay Gerken, as he embarks upon his retirement. Jay has most recently served as Chairman, President and Chief Executive Officer of the Fund and other funds in the Legg Mason complex. On behalf of all our shareholders and the Fund’s Board of Directors, I would like to thank Jay for his vision and guidance, and wish him all the best.

I am honored to have been appointed to my new role with the Fund. During my 23 year career in the financial industry, I have seen it evolve and expand. Despite these changes, keeping an unwavering focus on our shareholders and their needs remains paramount. This was a consistent focus of Jay’s, and I look forward to following his lead in the years to come.

As always, we remain committed to providing you with excellent service and a full spectrum of investment choices. We also remain committed to supplementing the support you receive from your financial advisor. One way we accomplish this is through our website, www.lmcef.com. Here you can gain immediate access to market and investment information, including:

·  Fund prices and performance,

·  Market insights and commentaries from our portfolio managers, and

·  A host of educational resources.

We look forward to helping you meet your financial goals.

Sincerely,

Kenneth D. Fuller

Chairman, President and Chief Executive Officer

June 28, 2013

Investment commentary

Economic review

The U.S. economy expanded over the twelve months ended May 31, 2013, but the pace was generally far from robust. U.S. gross domestic product (“GDP”)i growth, as reported by the U.S. Department of Commerce, was a tepid 1.3% in the second quarter of 2012. Economic growth accelerated to 3.1% in the third quarter, partially due to increased private inventory investment, higher federal government spending and moderating imports. However, economic activity sharply moderated in the fourth quarter, with GDP expanding an anemic 0.4%. This was driven by a reversal of the above factors, as private inventory investment and federal government spending weakened. Economic growth then improved, as the U.S. Department of Commerce’s final reading for first quarter 2013 GDP growth, released after the reporting period ended, was 1.8%. Accelerating growth was due, in part, to strengthening consumer spending, which rose 2.6% during the first quarter, versus a 1.8% increase during the previous quarter.

While there was some improvement in the U.S. job market, unemployment remained elevated throughout the reporting period. When the period began, unemployment, as reported by the U.S. Department of Labor, was 8.2%. Unemployment then generally declined and was 7.8% in September 2012. The unemployment rate then fluctuated between 7.8% and 7.9% over the next four months. Unemployment then fell to 7.7% in February, 7.6% in March and 7.5% in April, before edging up to 7.6% in May. In an encouraging sign, the number of longer-term unemployed has declined in recent months. In February 2013, more than 40% of the people without a job had been out of work for more than six months. This fell to 37.3% in May 2013.

Meanwhile, the housing market brightened, as sales generally improved and home prices continued to rebound. According to the National Association of Realtors (“NAR”), existing-home sales rose 4.2% on a seasonally adjusted basis in May 2013 versus the previous month and were 12.9% higher than in May 2012. In addition, the NAR reported that the median existing-home price for all housing types was $208,000 in May 2013, up 15.4% from May 2012. This marked the fifteenth consecutive month that home prices rose compared to the same period a year earlier. While the inventory of homes available for sale rose 3.3% in May 2013 to a 5.1 month supply at the current sales pace, it was 10.1% lower than in May 2012.

The manufacturing sector expanded during the majority of the reporting period, although it experienced several soft patches. Based on the Institute for Supply Management’s Purchasing Managers’ Index (“PMI”)ii, after expanding 34 consecutive months, the PMI fell to 49.7 in June 2012, which represented the first contraction in the manufacturing sector since July 2009 (a reading below 50 indicates a contraction, whereas a reading above 50 indicates an expansion). Manufacturing continued to contract over the next two months before ticking up to 51.5 in September and 51.7 in October. The PMI fell back to contraction territory with a reading of 49.5 in November. While manufacturing then expanded over the next five months, in May 2013 the PMI fell to 49.0, its lowest level since July 2009.

Growth generally moderated overseas and, in some cases, fell back into a recession. In its April 2013 World Economic Outlook Update, the International Monetary Fund (“IMF”) stated that “Emerging market and developing economies are still going strong, but in advanced economies, there appears to be a growing bifurcation between the United States on one hand and the euro area on the other.” The IMF projects that global growth will increase from 3.2% in 2012 to 3.3% in 2013. From a regional perspective, the IMF anticipates 2013 growth will be -0.3% in the Eurozone. Growth in emerging market countries is expected to remain higher than in their developed country counterparts, and the IMF projects that emerging market growth will increase from 5.1% in 2012 to 5.3% in 2013. In particular, China’s economy is expected to grow 8.0% in 2013, versus 7.8% in 2012. Elsewhere, the IMF projects that growth in India will increase from 4.0% in 2012 to 5.7% in 2013.

The Federal Reserve Board (“Fed”)iii took a number of actions as it sought to meet its dual mandate of fostering maximum employment and price stability. As has been the case since December 2008, the Fed

Investment commentary (cont’d)

kept the federal funds rateiv at a historically low range between zero and 0.25%. At its June 2012 meeting, the Fed announced that it would continue its program of purchasing longer-term Treasury securities and selling an equal amount of shorter-term Treasury securities (often referred to as “Operation Twist”) until the end of 2012. In September, the Fed announced a third round of quantitative easing (“QE3”), which involves purchasing $40 billion each month of agency mortgage-backed securities (“MBS”) on an open-end basis. In addition, the Fed further extended the duration that it expects to keep the federal funds rate on hold, until at least mid-2015. At its meeting in December, the Fed announced that it would continue purchasing $40 billion per month of agency MBS, as well as initially purchasing $45 billion a month of longer-term Treasuries. The Fed also said that it would keep the federal funds rate on hold “...as long as the unemployment rate remains above 6.5%, inflation between one and two years ahead is projected to be no more than a half percentage point above the Committee’s 2.0% longer-run goal, and longer-term inflation expectations continue to be well anchored.” At its meeting that ended on June 19, 2013, after the reporting period ended, the Fed did not make any material changes to its official policy statement. However, in a press conference following the meeting, Fed Chairman Bernanke said “...the Committee currently anticipates that it would be appropriate to moderate the monthly pace of purchases later this year; and if the subsequent data remain broadly aligned with our current expectations for the economy, we would continue to reduce the pace of purchases in measured steps through the first half of next year, ending purchases around midyear.” These comments initially triggered a sharp sell-off in both the stock and bond markets. While the stock market subsequently rallied and recouped its losses in early July, the bond market has not rebounded as sharply. As a result, Treasury yields remain higher than they were prior to Chairman Bernanke’s press conference.

Given the economic challenges in the Eurozone, the European Central Bank (“ECB”)v lowered interest rates from 1.00% to 0.75% in July 2012, at the time a record low. In September the ECB introduced its Outright Monetary Transactions (“OMT”) program. With the OMT, the ECB can purchase an unlimited amount of bonds that are issued by troubled Eurozone countries, provided the countries formally ask to participate in the program and agree to certain conditions. In May 2013, the ECB cut rates to a new record low of 0.50%. In other developed countries, the Bank of England kept rates on hold at 0.50% during the reporting period, as did Japan at a range of zero to 0.10%, its lowest level since 2006. In September, the Bank of Japan announced that it would increase its asset-purchase program and extend its duration by six months until the end of 2013. Then, in January 2013, the Bank of Japan announced that it would raise its target for annual inflation from 1% to 2%, and the Japanese government introduced a ¥10.3 trillion ($116 billion) stimulus package to support its economy. Elsewhere, with growth rates declining, both China and India lowered their cash reserve ratios for banks.

As always, thank you for your confidence in our stewardship of your assets.

Sincerely,

Kenneth D. Fuller

Chairman, President and Chief Executive Officer

July 5, 2013

All investments are subject to risk including the possible loss of principal. Past performance is no guarantee of future results. Forecasts and predictions are inherently limited and should not be relied upon as an indication of actual or future performance.

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Fund overview

Q. What is the Fund’s investment strategy?

A. The Fund’s primary investment objective is high current income and its secondary objective is total return. Under normal market conditions, the Fund invests in a global portfolio of securities consisting of below investment grade fixed-income securities, emerging market fixed-income securities and investment grade fixed-income securities. We have broad discretion to allocate the Fund’s assets among the following segments of the global market for below investment and investment grade fixed-income securities: corporate bonds, loans, preferred stock, mortgage- and asset-backed securities and sovereign debt, and derivative instruments of the foregoing securities. The Fund may use a variety of derivative instruments, such as options, futures contracts, swap agreements and credit default swaps, as part of its investment strategies or for hedging or risk management purposes.

At Western Asset Management Company (“Western Asset”), the Fund’s subadviser, we utilize a fixed-income team approach, with decisions derived from interaction among various investment management sector specialists. The sector teams are comprised of Western Asset’s senior portfolio management personnel, research analysts and an in-house economist. Under this team approach, management of client fixed-income portfolios will reflect a consensus of interdisciplinary views within the Western Asset organization. The individuals responsible for development of investment strategy, day-to-day portfolio management, oversight and coordination of the Fund are Stephen A. Walsh, S. Kenneth Leech, Michael C. Buchanan, Keith J. Gardner, Ryan K. Brist and Christopher F. Kilpatrick. It is anticipated that Mr. Walsh will step down as a member of the Fund’s portfolio management team effective on or about March 31, 2014.

Q. What were the overall market conditions during the Fund’s reporting period?

A. The spread sectors (non-Treasuries) overcame several periods of heightened risk aversion and generally outperformed equal-durationi Treasuries over the twelve months ended May 31, 2013. Risk aversion was prevalent at times given mixed economic data, contagion fears from the European sovereign debt crisis and uncertainties regarding future Federal Reserve Board (“Fed”)ii actions. However, periodic setbacks were often temporary in nature and spread sector demand was generally solid as investors looked to generate incremental yield in the low interest rate environment.

Both short- and long-term Treasury yields moved higher during the twelve months ended May 31, 2013. Two-year Treasury yields rose from 0.27% at the beginning of the period to 0.30% at the end of the period. Their peak of 0.30% occurred on several occasions and they were as low as 0.20% on April 29, 2013. Ten-year Treasury yields were 1.59% at the beginning of the period and peaked at 2.16% at the end of the period. On July 25, 2012, ten-year Treasuries closed at an all-time low of 1.43%.

The Barclays U.S. Aggregate Indexiii returned 0.92% for the twelve months ended May 31, 2013. Investment grade corporate bonds posted solid results, with the Barclay U.S. Credit Indexiv gaining 4.26%. Comparatively, riskier fixed-income securities produced robust returns. Over the fiscal year, the Barclays Capital U.S. Corporate High Yield — 2% Issuer Cap Index (the “Index”)v gained 14.82%. During this period, as measured by the Index, lower-quality CCC-rated bonds outperformed higher-quality BB-rated securities, returning 19.60% and 12.55%, respectively. In contrast, emerging market debt, as measured by the JPMorgan Emerging Markets Bond Index Global (“EMBI Global”),vi returned 10.41% for the twelve months ended May 31, 2013. At the same time, corporations domiciled in emerging market countries, as measured by the Barclays Emerging Market U.S. Dollar Corporate Index,vii returned 11.17%.

Q. How did we respond to these changing market conditions?

A. A number of adjustments were made to the Fund’s portfolio during the reporting period. We slightly increased the Fund’s modest allocation to investment grade corporate bonds and pared a small amount of its exposure to our largest

Fund overview (cont’d)

allocation, high-yield corporate bonds. However, within the high-yield allocation, we added to the Fund’s CCC-rated bonds based on valuations, the fundamental backdrop and our belief that CCC-rated bonds tend to have lower durations and would be less sensitive to changes in interest rates. Additionally, we reduced our exposure to BB-rated securities which typically have longer durations versus the high yield market. Within our emerging market allocation, we marginally reduced our sovereign exposure in favor of emerging market corporate bonds. We felt the latter would be more resilient in a rising rate environment and it offered better relative value. We also actively participated in the high yield and investment grade bond and emerging market new issue markets and purchased securities that we felt were attractively valued.

The Fund employed U.S. Treasury futures to manage its yield curveviii positioning and duration. They did not meaningfully impact the Fund’s performance during the reporting period.

Currency forwards were used to hedge the Fund’s currency risk and manage our non-U.S. dollar currency exposures. These hedges, which were intended to offset the decline or appreciation in the value of our euro bonds when translated back to U.S. dollars, were a small detractor from performance. Options on high-yield index swaps and high-yield index swaps were used to opportunistically manage the Fund’s exposure to the high-yield market. These “market hedges” were intended to protect the portfolio from periods of risk aversion, while maintaining the Fund’s exposure to higher betaix (and higher income) idiosyncratic investments. All told, these instruments detracted from performance.

During the reporting period, we tactically utilized leverage in the Fund. We ended the period with leverage as a percentage of gross assets, of approximately 21%, relatively unchanged during the twelve months ended May 31, 2013. The use of leverage was additive for results given the positive performance of high-yield bonds and emerging market debt.

Performance review

For the twelve months ended May 31, 2013, Western Asset Global High Income Fund Inc. returned 16.51% based on its net asset value (“NAV”)x and 12.77% based on its New York Stock Exchange (“NYSE”) market price per share. The Fund’s unmanaged benchmarks, the Barclays U.S. Aggregate Index, the Barclays U.S. Corporate High Yield — 2% Issuer Cap Index and the EMBI Global, returned 0.92%, 14.82% and 10.41%, respectively, for the same period. The Lipper High Yield (Leveraged) Closed-End Funds Category Averagexi returned 19.24% over the same time frame. Please note that Lipper performance returns are based on each fund’s NAV.

During the twelve-month period, the Fund made distributions to shareholders totaling $1.16 per share. The performance table shows the Fund’s twelve-month total return based on its NAV and market price as of May 31, 2013. Past performance is no guarantee of future results.

Performance Snapshot as of May 31, 2013

All figures represent past performance and are not a guarantee of future results.

* Total returns are based on changes in NAV or market price, respectively. Returns reflect the deduction of all Fund expenses, including management fees, operating expenses, and other Fund expenses. Returns do not reflect the deduction of brokerage commissions or taxes that investors may pay on distributions or the sale of shares.

† Total return assumes the reinvestment of all distributions at NAV.

‡ Total return assumes the reinvestment of all distributions in additional shares in accordance with the Fund’s Dividend Reinvestment Plan.

Q. What were the leading contributors to performance?

A. The Fund’s exposure to high-yield corporate bonds was the largest contributor to performance during the reporting period. Within the high-yield market, we had a bias for lower-quality CCC-rated bonds over higher quality BB-rated securities. This positioning was beneficial, given the significant outperformance of CCC-rated bonds versus their BB-rated counterparts. Our exposure to several high-yield bonds was also additive for performance during the reporting period. Examples of holdings that contributed to performance were Sprint Nextel Corp., Realogy Holdings Corp. and Wind Acquisition Holdings Finance. Bonds issued by Sprint Nextel Corp. (and Sprint Capital Corp.) rallied given their attractive valuation, as well as an improved outlook for the wireless competitive landscape and the pricing environment. In addition, Japan’s investment grade rated Softbank made a bid to acquire B-rated Sprint Nextel during the reporting period, sending Sprint Nextel’s bonds higher. Realogy Corp. has a diversified business model that includes real estate franchising, brokerage, relocation and title services. Its business units include Better Homes and Gardens Real Estate, CENTURY 21, Coldwell Banker, Sotheby’s International Realty and Title Resource Group. Investor sentiment for Realogy Holdings Corp. improved as there were signs of a sustainable recovery in the housing market. In addition, in October 2012 the company went public and raised more than $1 billion in additional capital, which will help support its debt obligations. Wind Acquisition Finance is the third largest wireless provider and the second largest wireline provider in Italy. Its bonds performed poorly earlier in the reporting period. We maintained our position, as we felt the weakness was primarily due to the fact that the company is located in Italy, a peripheral European country that was a key concern in the European sovereign debt crisis. As the period progressed, Wind Acquisition Finance’s bonds rebounded sharply, as its fundamentals remained intact and the European Central Bank (“ECB”)xii took actions to support peripheral European countries.

The Fund’s emerging market debt exposure also contributed to performance. In particular, the Fund’s Venezuelan hard currency sovereign debt and Mexican local sovereign debt generated strong results. Venezuelan hard currency sovereign bonds, which began the period at cheap valuations, benefited from higher oil prices and increased expectations that President Chavez would not be reelected. While Chavez was reelected in October 2012, it was not enough to offset the country’s sovereign bond’s earlier strong results. On March 5, 2013, Chavez died and Venezuelan hard currency sovereign debt rallied sharply. We believe valuations in Venezuela are still very attractive at a yield level of approximately 9% and our belief is that there are both ability and willingness for the country to meet its debt obligations. Mexican local sovereign debt was supported by improving economic growth, led by gains in the manufacturing sector. This also triggered solid demand for the Mexican peso. Allocation to Russia also benefited as Russian sovereign debt and corporate debt all generated strong returns.

Finally, the Fund’s allocation to investment grade corporate bond market contributed to absolute results. In particular, an allocation to Citigroup, Inc. benefited performance as investor sentiment improved due to continued balance sheet and capital ratio improvement, as well as strengthening fundamentals.

Q. What were the leading detractors from performance?

A. While the portfolio’s exposure to emerging market debt added to results on an absolute basis, within the asset class the Fund’s allocation to Latin American hard currency sovereign debt, in countries such as Brazil, Colombia, Mexico and Peru detracted from performance. Exposure to hard currency sovereign debt in Indonesia also detracted from performance. As previously discussed, emerging market sovereign debt is more sensitive to rising interest rates. With rates rising sharply during the period it negatively impacted the Fund’s sovereign debt exposure.

Within the high-yield bond market, the Fund’s relatively modest position in Seat Pagine Gialle SpA was not rewarded. Seat Pagine Gialle SpA is a directories publisher in Italy. The industry has been going through a structural decline over the last few

Fund overview (cont’d)

years given the shift in consumers’ preferences for using the Internet for local searches rather than traditional yellow pages and white pages. While the company’s Internet business has been growing, it has not been sufficient to offset the decline in print. In February 2013, Seat Pagine Gialle SpA missed an interest payment and the bond’s prices declined as markets were rising.

Finally, in the investment grade corporate bond market, having a position in Cliff’s Natural Resources, detracted from results. The company has suffered from a decline in prices for iron-ore and metallurgical coal that is used for producing steel and steel related products. During the first half of the reporting period, its bonds traded down from a premium to a slight discount. We decided to add exposure in November and December of 2012. Thus far in 2013, we have been pleased to see the company manage its balance sheet proactively. The company cut its equity dividend and sold additional common shares to maintain their investment grade rating profile. The market was still unimpressed and its bonds have moved modestly lower. We continue to hold our positions.

Looking for additional information?

The Fund is traded under the symbol “EHI” and its closing market price is available in most newspapers under the NYSE listings. The daily NAV is available on-line under the symbol “XEHIX” on most financial websites. Barron’s and the Wall Street Journal’s Monday edition both carry closed-end fund tables that provide additional information. In addition, the Fund issues a quarterly press release that can be found on most major financial websites as well as www.lmcef.com.

In a continuing effort to provide information concerning the Fund, shareholders may call 1-888-777-0102 (toll free), Monday through Friday from 8:00 a.m. to 5:30 p.m. Eastern Time, for the Fund’s current NAV, market price and other information.

Thank you for your investment in Western Asset Global High Income Fund Inc. As always, we appreciate that you have chosen us to manage your assets and we remain focused on achieving the Fund’s investment goals.

Sincerely,

Western Asset Management Company

June 14, 2013

RISKS: Fixed-income securities are subject to credit risk, inflation risk, call risk and interest rate risk. An investment in the Fund is subject to investment risk, including the possible loss of the entire principal amount that you invest. As interest rates rise, bond prices fall, reducing the value of the Fund’s holdings. The Fund may use derivatives, such as options, futures contracts, swap agreements and credit default swaps, which can be illiquid, may disproportionately increase losses and have a potentially large impact on Fund performance. Investing in foreign securities is subject to certain risks not associated with domestic investing, such as currency fluctuations, and changes in political, regulatory and economic conditions. These risks are magnified in emerging or developing markets. High yield bonds involve greater credit risk (risk of default) and liquidity risk than investment grade bonds. Leverage may magnify gains and increase losses in the Fund’s portfolio.

Portfolio holdings and breakdowns are as of May 31, 2013 and are subject to change and may not be representative of the portfolio managers’ current or future investments. Please refer to pages 9 through 31 for a list and percentage breakdown of the Fund’s holdings.

The mention of sector breakdowns is for informational purposes only and should not be construed as a recommendation to purchase or sell any securities. The information provided regarding such sectors is not a sufficient basis upon which to make an investment decision. Investors seeking financial advice regarding the appropriateness of investing in any securities or investment strategies discussed should consult their financial professional. The Fund’s top five sector holdings (as a percentage of net assets) as of May 31, 2013 were: Sovereign Bonds (24.1%), Energy (18.0%), Consumer Discretionary (15.7%), Financials (14.9%) and Materials (14.8%). The Fund’s portfolio composition is subject to change at any time.

All investments are subject to risk including the possible loss of principal. Past performance is no guarantee of future results. All index performance reflects no

deduction for fees, expenses or taxes. Please note that an investor cannot invest directly in an index.

The information provided is not intended to be a forecast of future events, a guarantee of future results or investment advice. Views expressed may differ from those of the firm as a whole.

Fund at a glance† (unaudited)

Investment breakdown (%) as a percent of total investments

Spread duration (unaudited)

Economic Exposure — May 31, 2013

Total Spread Duration

Spread duration measures the sensitivity to changes in spreads. The spread over Treasuries is the annual risk-premium demanded by investors to hold non-Treasury securities. Spread duration is quantified as the % change in price resulting from a 100 basis points change in spreads. For a security with positive spread duration, an increase in spreads would result in a price decline and a decline in spreads would result in a price increase. This chart highlights the market sector exposure of the Fund’s sectors relative to the selected benchmark sectors as of the end of the reporting period.

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Effective duration (unaudited)

Interest Rate Exposure — May 31, 2013

Total Effective Duration

Effective duration measures the sensitivity to changes in relevant interest rates. Effective duration is quantified as the % change in price resulting from a 100 basis points change in interest rates. For a security with positive effective duration, an increase in interest rates would result in a price decline and a decline in interest rates would result in a price increase. This chart highlights the interest rate exposure of the Fund’s sectors relative to the selected benchmark sectors as of the end of the reporting period.

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Schedule of investments

May 31, 2013

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Schedule of investments (cont’d)

May 31, 2013

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Schedule of investments (cont’d)

May 31, 2013

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Western Asset Global High Income Fund Inc.

See Notes to Financial Statements.

Schedule of investments (cont’d)

May 31, 2013

Western Asset Global High Income Fund Inc.