Exhibit 99.1

Contact:

Alan B. Lewis

Acclaim Entertainment, Inc.

(516) 656-5000

alewis@acclaim.com

FOR IMMEDIATE RELEASE

ACCLAIM ENTERTAINMENT, INC. APPOINTS

RODNEY COUSENS CHIEF EXECUTIVE OFFICER

Company Co-Founder, Gregory Fischbach, Resigns CEO Position and

Remains as Co-Chairman and Member of Board of Directors

GLEN COVE, NY, June 2, 2003 – Acclaim Entertainment, Inc. (NASDAQ.SC: AKLM), today announced that it has appointed Rodney Cousens as its new Chief Executive Officer. Cousens, who had been serving as the organization’s Global President and Chief Operating Officer, succeeds Acclaim’s co-founder, Gregory Fischbach, who has resigned the CEO position that he held since the Company’s inception in 1987. Fischbach will continue with the organization as Co-Chairman and member of its Board of Directors.

“We are entering a new era for this organization and I am very pleased to have Rod appointed as my successor,” said Gregory Fischbach, Co-Founder and Co-Chairman for Acclaim. “Given his impact on our organization since the beginning of this calendar year, I am confident that he will continue to utilize his industry knowledge and leadership skills to benefit the organization.”

“During the last five months, I have driven the process for our organization to adopt and implement a new global operating plan that is heavily focused on improving our core business practices, including reducing operating expenses, realigning our brand-driven product development strategy and managing our position at retail,” added Rod Cousens, Chief Executive Officer for Acclaim. “While this is an ongoing process, I believe that we have completed the foundation-building first phase that has set the stage for how we will conduct our business on a daily basis going forward. I will continue to strengthen our management team with leaders that are dedicated to this new structure, who possess the singular end-goal of facilitating our future growth and returning the organization to profitability.”

About Acclaim Entertainment

Based in Glen Cove, N.Y., Acclaim Entertainment, Inc., is a worldwide developer, publisher and mass marketer of software for use with interactive entertainment game consoles including those manufactured by Nintendo, Sony Computer Entertainment and Microsoft Corporation as well as personal computer hardware systems. Acclaim owns and operates five studios located in the United States and the United Kingdom, and publishes and distributes its software through its subsidiaries in North America, the United Kingdom, Australia, Germany, France and Spain. The Company uses regional distributors worldwide. Acclaim also distributes entertainment software for other publishers worldwide, publishes software gaming strategy guides and issues “special edition” comic magazines periodically. Acclaim’s corporate headquarters are in Glen Cove, New York and Acclaim’s common stock is publicly traded on NASDAQ.SC under the symbol AKLM. For more information please visit our website at www.acclaim.com.

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ACCLAIM/2

The statements contained in this release which are not historical facts, are “forward-looking statements.” Acclaim cautions readers of this press release that a number of important factors could cause Acclaim’s actual future results to differ materially from those expressed in any such forward- looking statements. These important factors, including, without limitation, the financial strength of the interactive entertainment industry, dependence on new product introductions and the ability to maintain the scheduling of such introductions, technological changes, dependence on major platform manufacturers and other factors that could affect Acclaim, are described in Acclaim’s Annual Report on Form 10-K for the fiscal year ended March 31, 2002, and Acclaim’s subsequent Quarterly Reports on Form 10-Q, all of which were filed with the United States Securities and Exchange Commission. Readers of this press release are referred to such filings.

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