Branislav Simić took up wrestling in his youth and switched weight classes several times, before settling on middleweight and the Greco-Roman style, in which he won the Yugoslavian national championship in 1952. This was his first of 11 national titles, missing only 1954 and 1962, the latter of which he did not participate in. He made his major international début at the 1955 World Championships, where he placed fifth, and then competed at the 1956 Melbourne Olympics, where he withdrew after the first round. He was also selected for the 1960 Rome Games, but did not start due to a shoulder injury.
Simić’s career then took an upswing, as he won silver at the 1963 World Championships, behind Tevfik Kış of Turkey. At the 1964 Tokyo Olympics, however, Kış was injured, and in his absence Simić reached the pinnacle of his career by capturing the gold medal. It was not the end of his career, however, as he placed sixth at the 1967 World Championships, won gold at that year’s Mediterranean Games, and captured a bronze medal at the 1968 Mexico City Olympics. He was also Yugoslavia’s flagbearer in the Opening Ceremony at the latter tournament. He later served as a wrestling referee, including at six consecutive editions of the Olympics, from 1984 through 2004, and by career was a history and geography teacher.