Career
On 28 October 2006, while playing for, Božović scored an equalizer in their home league fixture against Voždovac. In June 2007, Božović moved to, playing regularly for the team in the first six months. However, he lost his place in the starting eleven in the second half of the 2007-2008 season to his fellow countryman Mladen Božović, who arrived at the club in the 2008 winter transfer window.
In the summer of 2010, Božović was released by the club after receiving very little playing time in the previous two years.
In August 2013, Božović joined Hong Kong First Division side Happy Valley. On 5 January 2014, he was one of the seven players and coaching staff arrested by the Hong Kong Independent Commission Against Corruption (Independent Commission Against Corruption) for allegations with match-fixing.
On 6 January 2014, the homes of Božović and five other Happy Valley players were raided by the Independent Commission Against Corruption as the officials stepped up their investigation into alleged match-fixing. On 26 March 2014, Božović and other Happy Valley players went to the Hong Kong Labour Department to make claims against Happy Valley for unpaid and outstanding wages worth around 100,000 Hong Kong dollars.
Božović played two matches for the Montenegrin national team, making both appearances in 2007.
