Kasparov, a vocal critic of Vladimir Putin, was the sole challenger yesterday against Kirsan Ilyumzhinov, a wealthy businessman known to be supported by the Russian president.
The vote was held on the sidelines of an international tournament in Norway.
Delegates at the 2014 Chess Olympiad in the northern city of Tromsoe voted 110-61 in favor of Ilyumzhinov, with four votes annulled.
Ilyumzhinov, who once claimed to have visited an alien spaceship, has headed the governing body of chess, known by its French acronym FIDE, for 19 years.
The next year, the chess chief met President Bashar Assad in Syria as fighting escalated there, boosting speculation he was an unofficial representative for Russia, an Assad ally.