Born in Netherton, near Dudley, Worcestershire, Grosvenor started his football career with Stourbridge before moving to Birmingham in 1928. His early career was disrupted by injury, but once fit he took over at inside right and creator of chances when the ageing Johnny Crosbie moved on. In all he made 115 first team appearances for Birmingham and played three times for England in 1933, scoring twice. After leaving Birmingham he had short spells at Sheffield Wednesday and Bolton Wanderers 1937 to 1938, finishing up at local club Dudley Town in 1938. After football, he became a sheet-metal worker. He died in 1972 at the age of 63.