Washington D.C. 20549


Report of Foreign Issuer


Pursuant to Rule 13a-16 or 15d-16 of
the Securities Exchange Act of 1934

For period ending June 30, 2008

GlaxoSmithKline plc
(Name of registrant)


980 Great West Road, Brentford, Middlesex, TW8 9GS
(Address of principal executive offices)

Indicate by check mark whether the registrant files or
will file annual reports under cover Form 20-F or Form 40-F

Form 20-F x Form 40-F

Indicate by check mark whether the registrant by furnishing the
information contained in this Form is also thereby furnishing the
information to the Commission pursuant to Rule 12g3-2(b) under the
Securities Exchange Act of 1934.

Yes No x



GlaxoSmithKline plc - Share Buy-Back Programme

GlaxoSmithKline plc (the "Company") announces that it has today put in place an irrevocable, non-discretionary programme for the purchase of its Ordinary shares during the close period which precedes the 2008 second quarter results announcement, expected to be made on 23 July 2008.  The shares purchased on behalf of the Company are for cancellation.

The aim of the programme is to reduce the issued share capital of the Company to help enhance returns for shareholders.

The share buy-back programme will be managed by an independent third party which makes its trading decisions in relation to the Company's securities independently of, and uninfluenced by, the Company.

Any purchases pursuant to these arrangements will be effected during the period between 1 July 2008 and 23 July 2008
within certain pre-set parameters and in accordance with both the Listing Rules and the limitations of the repurchase authority granted to the Directors at the last Annual General Meeting of shareholders. The Company confirms that it currently has no inside information.

SM Bicknell
Company Secretary
30 June 2008



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


                                                             GlaxoSmithKline plc

Date: June 30, 2008

                                                                                                        By: VICTORIA WHYTE
                                                              Victoria Whyte
                                                 Authorised Signatory for and on
                                                   behalf of GlaxoSmithKline plc