Francis Grew was a layman, originally of good estate but impoverished by prosecutions for nonconformity in the high commission court and Star-chamber.
Obadiah was educated at Reading, under his uncle, John Denison, and was admitted a student at Balliol College, Oxford, in 1624, his tutor being Richard Trimnell.
Among the thirty parliamentary divines who crowded into Coventry for safety in 1642 were Richard Vines, rector of Weddington, Warwickshire, and Grew, his near neighbour.
In 1646 Grew took part with John Bryan in a public disputation on infant baptism at Trinity Church, with Hanserd Knollys and another.
Towards the end of 1648 Oliver Cromwell was in Coventry on his way to London from Scotland; Grew pleaded with him for the king's life.
In 1665, when the alarm of the plague thinned the pulpits throughout the country, Grew, like other nonconformists, began to hold public meetings for worship.
Captain Hickman of Barnacle, Warwickshire, unsuccessfully appeared as an informer against Grew, claiming a fine of £100 in the recorder's court.
At length in 1682 Grew, who had lost his eyesight, was convicted of a breach of the Five Mile Act, and imprisoned for six months in Coventry gaol.
While in prison, and in his retirement from Coventry after his release, he every week dictated a sermon to an amanuensis, who read it to four or five shorthand writers, each of whom got several copies made for use in twenty clandestine meetings.
Bishop Hacket offered him in 1662 a prebend at Lichfield in addition to the rectory of Caldecote, but he declined to conform, kept a school at Newington Green, and finally became the first minister (1698–1711) of the presbyterian congregation at Dagnal Lane, St. Albans, Hertfordshire.