Kullman made his professional ice hockey career debut with the Boston Bruins American Hockey League (AHL) affiliate, the Hershey Bears, during the 1948–49 AHL season.[2] In the following season, he was called up for a 14 game stint with the Boston Bruins of the National Hockey League, but was subsequently returned to Hershey on January 11, 1950.[4] Kullman continued his dominance of the American Hockey League and recorded seven consecutive 20 goal seasons until 1956.[5] Although his game slid after the 1955–56 season, he remained one of the few active 200 goal scorers and played on the Bears' penalty kill.[5] He had a career-high season during the 1953–54 campaign in which he recorded 81 points; 40 goals and 41 assists.[6]
Throughout his 12 seasons with the Bears, Kullman dominated the Hershey Bears and set multiple records before officially retiring in April 1960.[6] At the time of his retirement, Kullman ranked second in games played and goals, third in points, and fourth in assists.[7] Kullman died on June 11, 1999, in Hershey, Pennsylvania.[1]