He was employed as a boy at Covent Garden Theatre, but subsequently gained his chief celebrity as a scene-painter for Drury Lane Theatre and Her Majesty's opera-house.
When Clarkson Stanfield and David Roberts abandoned scene-painting, Grieve was left at the head of the profession.
His moonlight scenes were especially notable, and in 1832, after a performance of ‘Robert le Diable,’ the audience called him before the curtain, then an unprecedented occurrence.
Grieve also attained some success in small pictures and water-colours.
He died at South Lambeth on 12 November 1844, leaving a wife and five children.