He was educated at Eton and Trinity College, Cambridge.
He was Master of Magdalene College, Cambridge from 1813, and Dean of Windsor from 1846.
An Honorary Chaplain to the Queen, he was also registrar of the Order of the Garter.
In 1816 he married Charlotte, daughter of George Legge, 3rd Earl of Dartmouth.
Of their two sons, one (Ralph) was a Tory MP; the other (Frederick) was a priest, vicar of Butleigh and a prebendary at Wells Cathedral.
On being appointed Dean of Windsor in 1846, Neville-Grenville offered to resign the mastership of Magdalene, but was blocked by the Visitor, his brother Lord Braybrooke, who had earmarked the post for his fourth son Latimer Neville, then aged 19.
The Master's health was in decline: by 1850, although still only sixty years of age, he was "a wreck".
With some diplomacy needed to manage the Fellowship, the transition was achieved in 1853, and Latimer Neville became Master at the age of 26.Neville-Grenville died on 10 June 1854.