EXHIBIT 32.1

Certification of Principal Executive Officer

Pursuant to 18 U.S.C. 1350

(Section 906 of the Sarbanes-Oxley Act of 2002)

I, H. Thomas Watkins, President and Chief Executive Officer (principal executive officer) of Human Genome Sciences, Inc. (the “Registrant”), certify, to the best of my knowledge, based upon a review of the Annual Report on Form 10-K for the period ended December 31, 2011 of the Registrant (the “Report”), that:

(1) The Report fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, as amended; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

/s/ H. Thomas Watkins

Name: H. Thomas Watkins

Date: February 28, 2012