Played 13 NHL games with the Boston Bruins and 12 AHL seasons with Hershey Bears. He played junior for the Winnipeg Rangers and the Brandon Elks from 1943 to 1946 then transferred to the junior Stratford Kroehlers in 1946-47. In 1947-48 Kullman got into one game for the Boston Bruins. In 1949-50 the Bruins brought him up for 12 games when he scored an assist. Other than that he was playing in the minor pros. He played for the Hershey Bears from 1948-49 until his retirement in 1960. He won two Calder Cups (1958 & 1959) and was an offensive star for the team.