In 1972, Živković signed for Crvena zvezda of the Yugoslav First League.

Due to strong transfer regulations he missed entire 1972–73 season.

[1] He made his Yugoslav League debut for Crvena zvezda on 10 November 1973 in a win against OKK Beograd.

[2] He appeared in 203 games for the Zvezda during seven seasons and scored 2,838 points (13.9 PPG).

[3] Živković was a member of the Yugoslavian national team that won the gold medal at the 1975 Mediterranean Games in Algeria.