As so many of the municipalities of Sweden the present entity was created in 1971. The market town (köping) Grums (instituted as such in 1948) was amalgamated with Ed and the parish Värmskog from the dissolved Stavnäs Municipality, thus forming Grums Municipality.
The local political party is known as Grums medborgarparti, abbreviated gm. It was founded in 1994, in the wake of the short-lived unconventional party Ny Demokrati. The party was the municipality's third largest in the election of 1994 and 1998.