Grimshaw was born in Hyde, Cheshire in 1947 and studied at the Stockport College of Art from 1963 to 1968. He developed a unique style working in oils, charcoal and graphite to produce atmospheric, stylised images of the Northern industrial landscape, mainly in monochrome.
As a child he had a passion for steam engines and trainspotting, which continued into adulthood; for example he made the journey to the scrapyard at Barry in South Wales which held hundreds of steam locomotives awaiting scrapping, and made a personal photographic record of the occasion. Much of his work features steam engines.
Grimshaw exhibited widely in the UK (including at the Royal Scottish Academy and the Royal Academy in the 1970s) and in the US and Germany. His work was included in the private collections of L.S. Lowry, Edward Heath, the Warburton (Bread) Family and Gerald Kaufman MP., and he is represented in a number of public collections, including The Tate Gallery, Salford Art Gallery, Stockport Art Gallery and Bury Art Gallery.
He illustrated The Singing Street, a book of poems by Mike Harding, and executed limited edition lithographs for Christie's Contemporary Art. He also did the title slide images for the early BBC Great Railway Journeys of the World series. Artist Geoffrey Key described Grimshaw, a long time friend, as "one of the most important graphic artists working in the north during the last half of the 20th century".
While Grimshaw is most celebrated for his black and grey graphite portrayal of post-industrial Britain (e.g. canals, cityscapes, viaducts, steam trains) his portfolio included diverse other subjects such as megaliths, Stonehenge, quarries in North Wales, motorway construction and the solstices (often in combination). Colour treatment was largely reserved for Cheshire landscapes, and pictures of Clarice Cliff ceramics.
L.S.Lowry attended one of his earliest exhibitions, buying three of his major early works to hang alongside his small collection of Pre-Raphaelites. Grimshaw became a regular visitor to Lowry’s home in Mottram and could be described as one of Lowery’s appointed successors in portraying the north.
By the time of his death, in a house fire in 2001, Grimshaw had become an alcoholic and a reclusive figure. He held his last show in 1997 in the County Museum and Art Gallery at Prostejov, Moravia, Czech Republic, his 50th show in his 50th year. In 2004 a major retrospective exhibition was held at Stockport Art Gallery.