Barrow was born in London. He went to school first at Charterhouse, and subsequently to Felstead. He completed his education at Trinity College, Cambridge, where his uncle and namesake, afterwards Bishop of St Asaph, was a Fellow. He took to hard study, distinguishing himself in classics and mathematics; after taking his degree in 1648, he was elected to a fellowship in 1649; he then resided for a few years in college, and became candidate for the Greek Professorship at Cambridge, but in 1655 he was driven out by the persecution of the Independents. He spent the next four years traveling across France, Italy and even Constantinople, and after many adventures returned to England in 1659.

      In 1660, he was ordained and appointed to the Regius Professorship of Greek at Cambridge. In 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge.

      For the remainder of his life he devoted himself to the study of divinity. He was made a D.D. by royal mandate in 1670, and two years later Master of Trinity College (1672), where he founded the library, and held the post until his death.