Henry Cockburn (died 1476) was a 15th-century Scottish prelate. Between 1461 and 1476, he was the Bishop of Ross. On 23 March 1461 he received papal provision to the bishopric of Ross vacant by, presumably, the death of Thomas de Tulloch. He was consecrated sometime between 19 October 1463, when his name occurred in a Dunfermline Abbey document as bishop "elect and confirmed", and 16 August 1464, when he witnessed a royal charter as consecrated bishop.