FORM 6-K



                       SECURITIES AND EXCHANGE COMMISSION
                              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 April 01, 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

01 April 2008

GlaxoSmithKline plc (the 'Company') announces that in accordance with the
authority granted by shareholders at the Company's Annual General Meeting on 23
May 2007 it purchased 1,300,000 of its Ordinary shares of 25 pence each
('shares') on 1 April 2008 at a price of 1,097.46 pence per share.
The shares will be cancelled.

Following the cancellation of these shares, the Company holds 484,194,158 of its
shares in Treasury, representing 8.94% of the total voting rights in the
Company.

The Company has 5,418,738,050 shares in issue (excluding Treasury shares). This
number represents the total voting rights in the Company and may be used by
shareholders as the denominator for the calculations by which they can determine
if they are required to notify their interest in, or a change to their interest
in the Company under the Financial Services Authority's Disclosure and
Transparency Rules.

This announcement does not constitute, or form part of, an offer or any
solicitation of an offer to purchase or subscribe for securities in any
jurisdiction and is in conformity with the Financial Services Authority's
Disclosure and Transparency Rules.





SIGNATURES


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
                                                                    (Registrant)

Date: April 01, 2008                                      By: VICTORIA WHYTE
                                                              ------------------
                                                              Victoria Whyte
                                                 Authorised Signatory for and on
                                                   behalf of GlaxoSmithKline plc