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 March 31, 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 first quarter results
announcement, expected to be made on 23 April 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 April 2008 and 23 April 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

31 March 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: March 31, 2008                                          By: VICTORIA WHYTE
                                                              Victoria Whyte
                                                 Authorised Signatory for and on
                                                   behalf of GlaxoSmithKline plc