A putative class action in federal court in Newark claims rental-car giant Hertz Corp.’s parent misrepresented its finances to inflate its stock price when some owners were selling their shares.

The suit, brought Wednesday on behalf of people who bought the company’s stock, states that Hertz Global Holdings Inc.’s price surged between Feb. 25 and Nov. 4 amid a series of misleading statements—and fell after the company disclosed financial problems.