Grimes was the son of  Thomas Grimes, citizen and haberdasher of London and of Peckham and his wife Jane Muschamp daughter and co-heir of Thomas Muschamp, of Peckham. He was knighted at Hanworth, Middlesex on 2 June 1603.
Grimes, the son of Thomas Grimes, a London merchant, and Jane Muschamp, daughter and heir of Thomas Muschamp, both residents of Peckham, was knighted in Hanworth, Middlesex on June 2nd, 1603.