He was vicar of Biddenham, Bedfordshire, from 1808 to 1850, and with this living he held the rectory of Burton Latimer, Northamptonshire, from 1809 to 1843.
Grimshawe's first publication was 'The Christian's Faith and Practice,' &c. (Preston, 1813); followed by 'A Treatise on the Holy Spirit' (1815).
In 1822 he wrote a pamphlet on 'The Wrongs of the Clergy of the Diocese of Peterborough,' which was noticed by Sydney Smith in the 'Edinburgh Review' (article 'Persecuting Bishops').
In 1825 he issued 'An Earnest Appeal to British Humanity in behalf of Indian Widows.'
He published also a small volume of 'Lectures on the Future Restoration and Conversion of the Jews,' 1843, and several occasional sermons.