Sture Grahn represented Sweden in the 50 kilometers cross-country skiing event at the 1956 Cortino d’Ampezzo Olympics, where he placed 10th. His best years, however, were 1958 and 1962, where he won the 30 kilometers domestically and the 4x10 kilometers relay at the World Championships. In both relays he competed with Sixten Jernberg, but in 1958 he won gold alongside Lennart Larsson and Per-Erik Larsson, while in 1962 his other teammates were Lars Olsson and Assar Rönnlund. He was also a reserve at two other editions of the Olympics, but did not compete. He married two-time Olympic silver medalist Barbro Martinsson in 1968.