Grene, son of George Grene, probably a member of one of the Yorkshire families of the name, by his wife Jane Tempest, is said by Southwell to have been born in 1616 at Kilkenny in Ireland, to which country his parents had retired from their native land on account of the persecution; but the provincial's returns of 1642 and 1655 expressly vouch for his being a native of Kent.
After studying humanities in the college of the English Jesuits at St. Omer, he was admitted to the society in 1638.
In 1642 he was a professor in the college at Liege, and he held important offices in other establishments belonging to the English Jesuits on the continent.
After passing twelve years on the mission he was recalled to Watten, near Saint-Omer, to take charge of the novices.
He died there on 2 October 1667, leaving behind him the reputation of an eminent classic, historian, philosopher, and divine.