Exhibit 99.1

Catalyst Pharmaceutical Partners Announces Completion of Enrollment in CPP-109

Phase II(b) Clinical Trial for the Treatment of Cocaine Addiction

Top-Line Data Expected Early First Quarter 2013

CORAL GABLES, FL, May 21, 2012 — Catalyst Pharmaceutical Partners, Inc. (Nasdaq: CPRX) today announced that patient enrollment in its CPP-109 vigabatrin Phase II(b) clinical trial has reached its goal of 200 cocaine dependent subjects. The Company anticipates that screening of all remaining subjects will be completed this week and the total number enrolled will be approximately 210. Top-line results of the clinical trial are expected to be available early in the first quarter of 2013.

“We are pleased to have accomplished this important milestone in the development of CPP-109 by completing enrollment in the CPP-109 Phase II(b) clinical trial within the expected timeframe,” said Patrick J. McEnany, Chief Executive Officer of Catalyst. “There is a major need for effective and well-tolerated treatments for patients with cocaine addiction, and CPP-109 potentially represents a breakthrough product for them. I would like to thank our partners at the National Institute on Drug Abuse and the Veterans Administration, the clinical investigators and study site personnel for their dedication, as well as the subjects and their families who are participating in the trial.”

About the CPP-109 Phase II(b) Clinical Trial

The 24-week CPP-109 Phase II(b) clinical trial is randomized, double-blind and placebo-controlled. It is designed to demonstrate that the rate of cocaine dependent subjects treated with CPP-109, who abstain from cocaine use in the last two weeks of the trial’s treatment phase (weeks 8 and 9), will be higher than patients treated with placebo. Other outcomes include: i) reduction in cocaine use days; ii) increase in clean urines collected; and iii) durability of abstinence among those subjects who were abstinent during weeks 8 and 9.

About CPP-109 and Fast Track Status

CPP-109 is a GABA analog that is Catalyst’s designation for vigabatrin. Catalyst licensed CPP-109 from Brookhaven National Laboratory for the treatment of cocaine and other addictions, and has been granted “Fast Track” status by the U.S. Food and Drug Administration (FDA) for cocaine addiction. Under the Federal Food, Drug, and Cosmetic Act, the FDA is directed to facilitate the development and expedite review of drugs and biologics intended to treat serious or life-threatening conditions, and that demonstrate the potential to address unmet medical needs. Fast Track designation emphasizes communication between Catalyst and the FDA, and provides Catalyst benefits that may help to expedite the approval process. For example, Fast Track designation affords Catalyst the potential to submit an NDA for CPP-109 on a rolling or modular basis, allowing the FDA to review sections of the NDA in advance of receiving a full submission. The designation also means that Catalyst may have increased communications with the FDA regarding the design of its clinical studies, which may expedite the development and review of Catalyst’s application for the approval of CPP-109 for cocaine addiction and may provide greater certainty overall in the regulatory pathway.

About Cocaine Addiction

Cocaine binds to the dopamine reuptake transporter protein of the pre-synaptic neurons, preventing the reuptake and eventual breakdown of dopamine, resulting in enhanced and prolonged stimulation of dopamine on post-synaptic receptors, and causing a feeling of prolonged euphoria for the user. Cocaine addiction is caused by a neurological process called desensitization. Because the brain senses an unnaturally high level of dopamine, it responds by reducing the amount of dopamine released and the number of dopamine receptors created. Consequently, when the cocaine wears off, the user has a lower amount of dopamine and fewer functioning dopamine receptors, which results in a depressed mood. This desensitization process creates a lowering of mood each time the user takes more of the drug, causing them to seek additional cocaine to restore normal feelings, and requiring them to take an increasing amount of cocaine to achieve the same feeling of euphoria as before. According to the National Institute on Drug Abuse (NIDA), there are no pharmacologic treatments for cocaine addiction currently approved for marketing by the FDA.

According to the most recent Substance Abuse and Mental Health Services Administration (SAMHSA) survey, an estimated 1.5 million people, or 0.6% of the population aged 12 or over, had used cocaine in the month preceding the survey. Additionally, in 2010, approximately 637,000 people aged 12 or over had used cocaine for the first time within the preceding 12 months, an average of approximately 1,700 new users per day. In addition, approximately 699,000 patients received treatment for cocaine abuse in 2010.

Cocaine addiction is not only a U.S. health problem. In 2009, according to the United Nations Office on Drugs and Crime, there were 4.3 million – 4.7 million users of cocaine between the ages of 15 and 64 across Europe who had used it within the past year. Catalyst believes that the direct and indirect costs of cocaine use are indicative of a global public health problem, representing a significant unmet medical need for which no adequate pharmaceutical therapies exist.

About Catalyst Pharmaceutical Partners

Catalyst Pharmaceutical Partners, Inc. is a development-stage specialty pharmaceutical company focused on the development and commercialization of prescription drugs targeting

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diseases and disorders of the central nervous system, including addiction and epilepsy. Catalyst has two products in development, CPP-109 and CPP-115. It is currently evaluating its lead product and first-in-class GABA aminotransferase inhibitor candidate, CPP-109, for the treatment of cocaine addiction. Both CPP-109 and CPP-115 have been granted “Fast Track” status by the FDA for the treatment of cocaine addiction. Catalyst is also planning to evaluate CPP-109 for the treatment of other addictions. Catalyst believes that it controls all current intellectual property for drugs that have a mechanism of action related to the inhibition of GABA aminotransferase. For more information about Catalyst, go to www.catalystpharma.com.

Forward-Looking Statements

This press release contains forward-looking statements. Forward-looking statements involve known and unknown risks and uncertainties which may cause the Company’s actual results in future periods to differ materially from forecasted results. A number of factors, including whether CPP-109 will be safe and effective for the treatment of addiction, whether the CPP-109 Phase II(b) clinical trial will be successful, whether CPP-109 will ever be approved for commercialization, and those other factors described in the Company’s filings with the U.S. Securities and Exchange Commission (SEC), could adversely affect the Company. Copies of the Company’s filings with the SEC are available from the SEC, may be found on the Company’s website or may be obtained upon request from the Company. The Company does not undertake any obligation to update the information contained herein, which speaks only as of this date.

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