Barbor was commissioned lieutenant on 23 February 1756, and from 1758 commanded the sloop Postillion 18, an ex-French privateer, serving in the North Sea. He was posted captain of the Kennington 20 on 4 June 1759, and he served in the Mediterranean and commanded her until the end of 1763.
He did not enjoy any further employment until appointed to the French-built Belleisle 64 in early 1779, sailing for the East Indies in the following month and departing Madras in April 1780 with a convoy that arrived at Crookhaven in the south of Ireland in January 1781.
During the autumn of 1781 Barbor recommissioned the Fame 74 which went out to the Leeward Islands with Admiral Sir George Rodney in December 1781, and he fought at the Battle of the Saintes on 12 April 1782 where his ship suffered fifteen casualties.
Barbor died on 15 June 1782 in the West Indies having shown the first signs of a fever just six days previously.
He was married with at least two daughters.