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, 2004 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 15, 2005