Born at Sugworth, in the parish of Radley, Berkshire (now Oxfordshire), about 1509, he was admitted a probationer fellow of Corpus Christi College, Oxford, in 1528, graduated B.A.
He was Greek reader in his college, and was appointed Hebrew professor of the university about 1538, in succession to Robert Wakefeld.
In April 1542 he obtained permission from the university to expound in the public schools the Book of Genesis in the Hebrew language, 'provided that he lectured in a pious and catholic manner.'
When his death became known at Oxford many learned men composed Greek and Latin verses to his memory, and pasted them on the doors of St. Mary's Church.
These verses, together with some of Shepreve's own compositions, were collected with a view to their publication, under the editorship of George Etheridge, but they never appeared in print.