A well-known hedge-fund manager is taking a novel approach to making money: filing and publicizing patent challenges against pharmaceutical companies while also betting against their shares.

Kyle Bass, head of Hayman Capital Management LP—which made a fortune wagering on the housing bust—is targeting patents that he says have little value other than to drive up prescription drug prices. His new fund bets against companies whose patents it believes are spurious, and invests in those that would profit if the patents are invalidated, said people familiar with the matter.

His latest challenge seeks to employ a relatively new and inexpensive petition process to invalidate a Jazz Pharmaceuticals PLC patent for Xyrem, a narcolepsy drug with sales of $779 million last year, two-thirds of Jazz’s 2014 revenues.

Mr. Bass created the Coalition for Affordable Drugs, an organization that is the lead petitioner in several patent challenges filed with the U.S. Patent and Trademark Office. He says he plans to pursue the cases regardless of share price moves. “We will not settle,” he said in an interview.

Jazz Pharmaceuticals, of Dublin, Ireland, didn’t respond to requests for comment on Tuesday.