Predojević was a member of the silver medal-winning team ŠK Bosna Sarajevo at the European Club Cup in 2004. In addition to his three Cadet Championships in FR Yugoslavia, he was also Cadet Champion of Republika Srpska 10 times between 1997–2004, Youth Champion of both Republika Srpska and Bosnia and Herzegovina in 2005 and Junior Champion of Bosnia and Herzegovina three times (2001, 2003, 2004). He represented Bosnia and Herzegovina in Chess Olympiads in 2004, 2006, 2008, 2010 and 2014. In the 2008 event he achieved a rating performance of 2745, the fourth best at board 2.