Branković was the gold medallist over 400 metres at the 1992 European Athletics Indoor Championships, a feat which gained him the "Golden Badge" as the Спорт newspaper's Yugoslav sportsperson of the year.

He set Yugoslavian records in the 4×400 metres relay and remains the holder of a variety of indoor and outdoor Serbian national records in distances from 100 metres to 400 m. Born in Obrenovac in Belgrade and affiliated with the city's athletic club, AK Partizan, he made his first appearance on the world stage representing the Socialist Federal Republic of Yugoslavia.

Forming part of the 4×400 metres relay team at the 1987 World Championships in Athletics, he ran a national Yugoslavian record time of 3:03.30 minutes with Branislav Karaulić, Slobodan Popović and Ismail Mačev.

Another Yugoslavian relay record came for him at the 1991 World Championships in Athletics: competing in a team which also featured Dejan Jovković, Nenad Đurović and Mačev, he reached the final of the competition with the country's first sub-three-minute mark for the event (2:59.95 min).

He won the 400 m gold medal at the 1992 European Athletics Indoor Championships – an achievement which proved to be the pinnacle of his individual running career.