He earned the title of International Master by winning the 1981 World Junior Championship.

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.

In the late 1980s, these included Wolfsberg 1986, Prague 1987, Pula 1987 and 1988, Mendrisio 1987, 1988 and 1989, San Bernardino 1987, Belgrade 1987, Geneva 1988, Bela Crkva 1988, Oberwart 1988, Chiasso 1989, and Vrsac 1989.