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, 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, 2005 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: March 14, 2006