Graham was utility player but played mostly as a ruckman. Over the course of his career he was one of the few players who used the place kick and he played in losing grand finals with South Melbourne in 1936 and 1945. He polled well in a couple of Brownlow Medal counts with a seventh placing in 1937 and an equal sixth in 1941. He later served as coach of South Adelaide and also played briefly for the club.
His shin was lacerated in a football game, and the wound never healed properly. He had surgery after retirement to repair the wound and died from surgical complications. His son Ricky Graham and grandson Ben Graham both became league footballers at Geelong.