Craven was commissioned lieutenant on 31 December 1778, and in 1782 he commanded the cutter Flying Fish in that rank, bringing the first news of the Dutch fleet’s exit from the Texel during the Channel Fleet campaign of April-August. Unfortunately the cutter went aground off Dunkirk on 3 December and was seized by French troops, following which she was successfully refloated by the French to be commissioned into their service as the Poisson Volant.
He commissioned the troopship Gorgon 44 in the autumn of 1787 and remained with her until she was paid off towards the end of the following year. Having been promoted commander on 21 September 1790, he had the Marlborough 74 with the flag of Rear-Admiral Samuel Pitchford Cornish when she went out to the West Indies in October during the Spanish Armament, retaining her through to the following February. He then had the sloop Nautilus 16 going out to Newfoundland in July 1791 before leaving her within the year.
Following the outbreak of hostilities with revolutionary France, Craven commanded the Trimmer 14 on the Jersey station from May 1793, but his ship was found to be un-seaworthy shortly afterwards and was decommissioned. He was posted captain of the Woolwich 44 on 17 December although it appears he did not remain with her for long. His next command was the recently captured Dutch vessel Wassenar 66 which was commissioned as a troopship, serving in the Downs from March 1798 until 1800, and briefly flying the flag of Admiral Joseph Peyton.
His last command was the Glory 98 from October 1804 until April 1805, serving in the Channel and later flying the flag of Vice-Admiral Sir John Orde off Cadiz.
In 1808 Craven left the command of the Sea Fencibles on the River Medway to become the governor of the Royal Hospital at Haslar, retaining this post until 23 February 1820.
In the autumn of 1808 at Colchester, Essex, he married the widow of Reverend John Moore Brooke of Falkingham and Helpringham, Lincolnshire, this lady being the daughter of Captain William Judd of the navy.