Paul Tudor Jones for years charged some of the highest fees in the hedge-fund industry. Now the billionaire is cutting them for the second time in eight months.

The move is a dramatic retreat by one of Wall Street’s best-known investors. The former cotton trader rose to fame with a big score during 1987’s stock-market crash.

His fund’s only annual loss in the past three decades came during the 2008 financial crisis.

But in recent years, clients have pulled billions from Tudor Investment Corp. as Mr. Jones struggled to equal the profits of earlier years. Last summer, the firm eliminated 15% of its staff. Its flagship fund was roughly flat in 2016 despite a run-up in the U.S. stock market.

Some of Tudor’s wealthy investors objected to paying hefty fees to the hedge fund without gaining much profit in return, people close to the firm said.