Cvitan was born in Šibenik (then Yugoslavia). He made his debut for Yugoslavia's C team at the 1990 Chess Olympiad, held in Novi Sad, recording a plus score on board one. At the Manila Olympiad of 1992, he played on the second reserve board for Croatia and earned an individual gold medal. Cvitan competed in the FIDE World Chess Championship 2002, where he was knocked out in the first round by Alexander Lastin.