Mithat Bayrak took up wrestling in 1948 and first competed internationally at the 1955 Mediterranean Games, where he finished fourth in Greco-Roman welterweight. Wrestling in Greco-Roman welterweight for most of his career, Bayrak had a brief, but successful, international career. He won Olympic golds in 1956 and 1960 and won silvers at the 1959 Mediterranean Games (in welterweight) and at the 1959 Balkan Championships (in middleweight). Bayrak also competed at the 1958 World Greco-Roman Championships, where he finished 10th in middleweight. Bayrak retired after the 1960 Olympics, although he made a brief comeback to compete at the 1964 Olympics, where he was eliminated after the third round. In 1961, Bayrak emigrated to Germany, and settled in Witten, where he ran several restaurants with his wife. Joining KSV Witten 07 wrestling club, Bayrak continued to wrestle in local tournaments for almost 20 years and later worked as a wrestling coach with KSV Witten 07. Bayrak was inducted to FILA International Wrestling Hall of Fame in 2011.