Exhibit 99.1

PRESS RELEASE

HUMAN GENOME SCIENCES ANNOUNCES ADOPTION OF

SHORT-TERM STOCKHOLDER RIGHTS PLAN

ROCKVILLE, Maryland – May 17, 2012 – Human Genome Sciences, Inc. (NASDAQ: HGSI) (“HGS” or the “Company”) announced today that its Board of Directors has adopted a Stockholder Rights Plan (the “Rights Plan”) and declared a dividend of one share purchase right (a “Right”) for each share of HGS’s common stock (the “Common Stock”) held of record at the close of business on May 29, 2012.

The Company’s Board is committed to maximizing shareholder value through its previously announced strategic review process. The Rights Plan, which has a term of one year, is intended to allow the Company to fully engage in its strategic review process and as a means to protect the long-term interests of the Company’s stockholders. The Rights Plan will not prevent any offers or transactions that the Board determines to be in the best interest of HGS and its stockholders.

The Rights, which will initially trade with the Common Stock and represent the right to purchase one one-hundredth of a share of the new Series A Junior Participating Preferred Stock (the “Preferred Stock”) at $37.50 per Right, become exercisable on the tenth business day after a person or group acquires or commences a tender offer or exchange offer following the date of the Rights Plan for 15% or more of HGS’s Common Stock without prior Board approval or immediately prior to the acceptance for payment of Common Stock tendered pursuant to any tender offer or exchange offer commenced by a third party prior to the date of the Rights Plan. Under the Rights Plan, ownership of HGS’s Common Stock in the form of derivative securities counts towards the 15% ownership threshold.

Once exercisable, the Rights permit HGS stockholders, other than the acquiror, to purchase HGS Common Stock having a market value of twice the exercise price of the

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Rights, in lieu of the Preferred Stock. Alternatively, when the Rights become exercisable, the Board of Directors may authorize the issuance of one share of HGS Common Stock in exchange for each Right that is then exercisable. In addition, in the event of certain business combinations, the Rights permit the purchase of the Common Stock of an acquiror at a 50% discount. Rights held by the acquiror will become null and void in each case. At any time prior to ten business days after a person or group acquires 15% of more of the Common Stock, the Rights can be redeemed for $0.01 each by action of the Board.

The Rights expire on May 29, 2013 unless earlier redeemed, exchanged or terminated by the Company. The Rights distribution will not be taxable to stockholders and will be payable to stockholders of record on May 29, 2012.

The full text of the Rights Plan will be filed with the Securities and Exchange Commission.

ABOUT HUMAN GENOME SCIENCES

Human Genome Sciences exists to place new therapies into the hands of those battling serious disease.

For more information about HGS, please visit the Company’s web site at www.hgsi.com. Health professionals and patients interested in clinical trials of HGS products may inquire via email to clinicaltrialsinfo@hgsi.com or by calling HGS at 1-240-314-4430.

HGS, Human Genome Sciences and BENLYSTA are trademarks of Human Genome Sciences, Inc. Other trademarks referenced are the property of their respective owners.

SAFE HARBOR STATEMENT

This announcement includes statements that are forward-looking within the meaning of the Private Securities Litigation Reform Act of 1995. These forward-looking statements are based on our current intentions, beliefs and expectations regarding future events. We cannot guarantee that any forward-looking statement will be accurate. Investors should realize that if underlying assumptions prove inaccurate or unknown risks or uncertainties materialize, actual results could differ materially from our expectations. Investors are, therefore, cautioned not to place undue reliance on any forward-looking statement. Any forward-looking statement speaks only as of the date of this announcement, and, except as required by law, we do not undertake to update any forward-looking statement to reflect new information, events or circumstances.

Some important factors that could cause our actual results to differ from our expectations in these forward-looking statements include: our lack of commercial experience and

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dependence on the sales growth of BENLYSTA; any failure to commercialize BENLYSTA successfully; the occurrence of adverse safety events with our products; changes in the availability of reimbursement for BENLYSTA; the inherent uncertainty of the timing, success of, and expense associated with, research, development, regulatory approval and commercialization of our pipeline products, including darapladib and albiglutide, and new indications for existing products; substantial competition in our industry, including from branded and generic products; the highly regulated nature of our business; uncertainty regarding our intellectual property rights and those of others; the ability to manufacture at appropriate scale, and in compliance with regulatory requirements, to meet market demand for our products; our substantial indebtedness and lease obligations; our dependence on collaborations over which we may not always have full control; foreign exchange rate valuations and fluctuations; the impact of our acquisitions and strategic transactions; changes in the health care industry in the U.S. and other countries, including government laws and regulations relating to sales and promotion, reimbursement and pricing generally; significant litigation adverse to the Company, including product liability and patent infringement claims; our ability to attract and retain key personnel; and increased scrutiny of the health care industry by government agencies and state attorneys general resulting in investigations and prosecutions.

The foregoing list sets forth many, but not all, of the factors that could cause actual results to differ from our expectations in any forward-looking statement. Investors should consider this cautionary statement, as well as the risk factors identified in our periodic reports filed with the SEC, when evaluating our forward-looking statements.

IMPORTANT INFORMATION FOR INVESTORS AND STOCKHOLDERS

This communication does not constitute an offer to buy or a solicitation of an offer to sell any securities. In response to the tender offer commenced by GlaxoSmithKline plc through its wholly owned subsidiary, H. Acquisition Corp., HGS is filing a solicitation/recommendation statement on Schedule 14D-9 with the SEC. INVESTORS AND STOCKHOLDERS OF HGS ARE URGED TO READ THE SOLICITATION/RECOMMENDATION STATEMENT AND OTHER DOCUMENTS FILED WITH THE SEC CAREFULLY IN THEIR ENTIRETY (WHEN THEY BECOME AVAILABLE) BECAUSE THEY CONTAIN IMPORTANT INFORMATION. Investors and stockholders may obtain a free copy of these documents free of charge at the SEC’s website at www.sec.gov. HGS also will provide a copy of these materials without charge on its website at www.hgsi.com., or stockholders may call the company’s Information Agent, Innisfree M&A Incorporated, toll-free at 877-717-3926.

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Susannah Budington

Director, Corporate Public Relations

301-545-1062

Additional Contacts:

Joele Frank / Dan Katcher / Jamie Moser

Joele Frank, Wilkinson Brimmer Katcher

(212) 355-4449

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