Živković started playing handball at his hometown club Železničar Niš, before moving to Crvenka.

In his second tenure as head coach of FR Yugoslavia, Živković led the team to a third-place finish at the 1999 World Championship.

[1] After placing seventh in the 2000 Summer Olympics, Živković reached the semi-finals at the 2001 World Championship, losing in the bronze medal match to FR Yugoslavia.

[4] In February 2005, Živković was appointed as head coach by Macedonia for the nation's Euro 2006 qualifiers in June.

[5] He would take charge at Macedonian club Vardar during the summer,[6] but left for personal reasons in October of the same year.