Kvanmo joined local politics in Rana, and in 1973 she was elected to the Storting, representing the Socialist Left Party (SV). From 1977 she served as the parliamentary leader for the party. In 1975 and 1981 she was also a delegate to the UN general assembly. From 1985 to 1989, her "vararepresentant" was Asle Amundsen. She retired from parliament in 1989. From 1991 to 2002, she was a member of the Norwegian Nobel Committee, serving as the committee's vice chairman 1993-1998.