Grimshaw was born in Hyde, Cheshire in 1947 and studied at the Stockport College of Art from 1963 to 1968. He spent much of his working career at Manchester advertising agency Stowe Bowden Ltd.


By the time of his death in a house fire in 2001, Grimshaw had become an alcoholic and a reclusive figure.


In 2004 a major retrospective exhibition was held at Stockport Art Gallery in celebration of his life and work.