James William Travers Grimshaw (17 February 1912 – 26 September 1944) was an English cricketer who played first-class cricket between 1932 and 1936. Grimshaw was born in Darlington, County Durham in 1912 and attended King William's College on the Isle of Man before going up to Cambridge University. He gained a cricket Blue and played for the University cricket team, making his debut in the 1932 season.