Innes was commissioned lieutenant on 26 July 1739.
After being promoted commander of the sloop Ferret 14 on 14 November 1752 he brought her back from Jamaica in the following August and paid her off. From February 1755 he had the Otter 14, seeing service off Brest that summer. The future Admiral Francis Samuel Drake served as a lieutenant aboard this vessel but fell out with Innes and sought a position elsewhere.
Innes was posted captain of the Monmouth 70 on 25 June 1756, serving in the Channel under Vice-Admirals Sir Edward Hawke and Hon. Edward Boscawen, and removing in the following year to the Mermaid 20 on the same station. From 1758 he commanded the Enterprise 44, going out to Jamaica in May and returning home with a convoy which arrived in the Downs in July 1761. In 1762 he joined the Hampton Court 64, going out to the West Indies in March and joining the Defiance 60, Captain George Mackenzie, in the capture of the Spanish ships Venganza 26 and Marte 18 in Mariel Bay Hispaniola on 28 May. He then took part in operations against Havana from June-August, before returning to Plymouth and paying the Hampton Court off in December 1763.
Innes was the regulating captain at Dartmouth during the Falkland Islands dispute of 1770, but did not enjoy any further employment until the latter part of 1778 when he was appointed to the Queen 90. Serving in the Channel, he was present in the Channel fleet retreat of August 1779 and remained with the Queen until promoted rear-admiral on 26 September 1780, having participated in the Channel Fleet campaign from June.
In 1784 he went out to Jamaica as commander-in-chief with his flag flying aboard the Europa 50, Captains Edward Tyrell Smith, and from October 1784 Richard Fisher, but he died whilst in office on 21 January 1786.
Innes daughter Susannah married the future Major-General George Dyer. He lived his later years in Plymouth and was a very religious man who preached sermons to the crew of the Queen in the absence of a chaplain, apparently preferring this method of character improvement to that of corporal punishment.