He was born at Spalding, Lincolnshire, on 12 October 1724, the only surviving son, by his first wife, of Timothy Neve the antiquary.
He was admitted at Corpus Christi College, Oxford on 27 October 1737, at the age of thirteen, and was elected scholar in 1737 and fellow in 1747.
In 1759 he was one of the preachers at the Chapel Royal, Whitehall, and on 23 April in that year he was instituted, on the nomination of John Green, bishop of Lincoln, to the rectory of Middleton Stoney, Oxfordshire, which he resigned in 1792 in favour of his son, the Rev.
From 1783 to his death in 1798 Neve held the Lady Margaret professorship of divinity at Oxford and the sixth prebendal stall in Worcester Cathedral.
Neve's chief works were: Six letters addressed to him by Maurice Johnson on antiquarian topics were printed in the Bibliotheca Topographica Britannica, iii.