Initially starting out as an all-round track and field athlete, Martin Mølster later focused on the shot put and won six Norwegian titles in the event. Mølster won his first medal at the national championships in 1922 with silver in the pentathlon. The following year he won his first national title in the shot put before winning another five titles during his career (1926–29, 1931). In 1924 he did the double by winning national titles in the pentathlon and the decathlon, before winning a second pentathlon title in 1926. Mølster also competed in the pentathlon at the 1924 Paris Olympics where he came 11th.