Grimshaw's work has been exhibited at Rainyday Gallery, Penzance, and Penwith and Belgrave Galleries, St Ives. Originally Martin trained at Camberwell School of Arts and Crafts, and was awarded an MA in Fine Art from Falmouth College of Art in 2000. He comments: 'Often I work directly from the model or in the landscape. However, where the experience is a fleeting one, I make quick sketches, and then in the studio, allow the painting process to realise something I did not ‘know’ or had forgotten, about for example walking on the west coast of the Lizard where I live, or standing absorbing the stillness of the old cathedral-mosque of Cordoba, Spain.'

He organizes the life class for Lizardart, and is also a member of the Newlyn Society of Artists.