Penn was born in St. Thomas Parish, Bristol to Giles Penn and Joan Gilbert. On 6 June 1643 he married Margaret Jasper, a daughter of a wealthy Dutch merchant from Rotterdam. They had three children: Margaret, Richard and William. After 1650 he was employed as commander in chief of the southern fleet in the Atlantic and in the Mediterranean in pursuit of the Royalists under Prince Rupert. He was so active on this service that when he returned home on 18 March 1651 he could boast that he had not put foot on shore for more than a year.