Graham served the longest consecutive term of anyone in the history of the Legislative Assembly of New Brunswick, being re-elected in 1970, 1974, 1978, 1982, 1987, 1991 and 1995.
Graham served in the cabinets of Frank McKenna and Ray Frenette but resigned his seat in 1998 and in the subsequent Kent County by-election, the community continued to support the Graham family and his son Shawn Graham was elected as MLA in 1998 and would go on to become leader of the Liberals in 2002, and win the 2006 election.
During his political career, Graham served on numerous Legislative Committees.
While in opposition, he acted as critic for Agriculture, Natural Resources, Housing, Health, and Alcoholism and Drug Dependency.
He has been a Trustee of the Nature Conservancy of Canada, a member of the Board of the Atlantic Salmon Federation and an Honorary President of the Atlantic Canada Woodworking Centre of Excellence.