He was the son of Paul Neve, bailiff of the same place, and was educated at Ludlow school.
To this society he communicated several papers, including, in 1727, essays on the invention of printing and our first printers, and on Bishop Kennett's donation of books to Peterborough Cathedral.
Leaving Spalding about 1729, when a successor at the school was appointed, he moved to Peterborough, where he was minor canon from 24 March 1728–9 till 1745.
For twenty-eight years (1729–57) he was rector of Alwalton, Huntingdonshire, a living attached to his Lincoln prebend.
He died there on 3 February 1757, and was buried in Alwalton Church, in the north transept of which is an epitaph to his memory.
Mr. Greene of Drinkstone, Bury St. Edmunds, and sister to Lady Danvers of Rushbrooke, Suffolk.