Gustaf Kilman was the son of an army major and graduated from secondary school in Stockholm in 1901. He served as a lieutenant in the Royal Göta Artillery Regiment, which was based in Göteborg (Gothenburg). Kilman had a long career in equestrian events, winning his first major tournament, the Gyllene Hästen (Golden Horse) on his horse Lord Prime. Four years later he was a member of the Swedish show jumping team winning gold on his horse Gåtan at the Stockholm Olympics. In 1920, he had his second Olympic appearance in Antwerpen. This time, he only placed a joint 15th in the individual event. In 1921, he is mentioned as captain in the Svea Artillery Regiment. For his services he was made a Knight of the Order of the Sword and was awarded the Belgian Military Cross.
In 1915, Gustaf Kilman married Ellen Carolina Willerding, whom he later divorced. The had one son and one daughter. Then, Elin Gereonia Viktoria Karlsson became his partner. With her, Kilman had another daughter. In 1946, he committed suicide by shooting himself.