Levent Erdoğan began his weightlifting career by becoming the Turkish champion in 1978. Erdoğan had further success as a flyweight in international competitions, including winning gold at the Mediterranean Games in 1983 and 1987. In 1983 he also won silver at the Balkan Games, with these performances earning him a place on the Olympic team. At the 1984 Los Angeles Games he lifted 215.0 kg to finish eighth. He returned to the Olympics for the 1988 Games in Seoul, this time placing 16th. After his sports career Erdoğan worked as a coach for the national team before becoming the Vice-President of the Beşiktaş Gymnastics Club.