He is best remembered for scoring an extra time goal for Partizan against Sporting Clube de Portugal in the 2002–03 UEFA Cup first round.
In the 2003–04 season, he played with Sartid Smederevo, scoring six league goals in 19 appearances.
In 2009, Živković traveled to Australia for a trial with A-League club Central Coast Mariners.
[2] However, he signed with the Serbian-backed club Bonnyrigg White Eagles, playing in the NSW Premier League.
In 2012, Živković signed to play with Popinci in the Vojvodina lower league.