George Grimshaw (January 26, 1839 — January 21, 1898) was an English cricketer. He played first-class cricket for Lancashire. He was born in Audenshaw and died in Grafton.
Grimshaw played club cricket with Ashton-under-Lyne from 1863 onwards. Grimshaw made his first and only first-class appearance in 1868 against Marylebone Cricket Club. Grimshaw scored a duck in the first innings as a lower-order batsman, and when moved up to the opening order, scored 11 in the second innings.