Born in Lviv in 1899, Polish cyclist Feliks Kostrzębski represented several clubs in his hometown in the interwar period. In 1924 Kostrzębski was selected to compete at the 1924 Paris Olympics where he came 55th in the individual road race, almost two hours behind the winning time. He continued to compete for a few years after the Games, having a best result of third at the 1927 Polish national road race championships. The following year Kostrzębski rode in the Tour of Poland, where he came 41st in the general classification.