After a collegiate career with the
University of Denver during which he was named a First Team All-American, Grahame was signed by the
Houston Aeros of the WHA. He played a season for the minor league
Macon Whoopees in 1973 before coming up to the Aeros at the end of the season. He won in his opening debut with a shutout. In the 1974–75 season he made the Aeros for good, leading the WHA in wins, shutouts and goals against average and backstopping the club to the
AVCO World Trophy, winning both the
Ben Hatskin Trophy for best goaltender, First Team All-Star accolades and the
WHA Playoff MVP. His following two seasons saw an equal degree of success, including a Second Team All-Star berth in 1976 and a second Hatskin award in 1977. He became a free agent after the 1977 season and signed with the NHL's
Boston Bruins for the
1977–78 NHL season. He continued his starring play, having a fine season as the Bruins' number one goaltender. After that season, however, he was traded to the
Los Angeles Kings for a first-round draft pick in the 1979 draft (which turned into
Ray Bourque), and played poorly thereafter. He served with the Kings for three seasons before being sold to the
Quebec Nordiques in December,
1980. He played eight games for the Nordiques before being sent down to the minors for the remainder of the season, after which he retired. ==Post-playing career==