Captain George Cockburne (died 20 July 1770) was a naval administrator, who went on to be Comptroller of the Navy.
Cockburne was appointed Comptroller of the Navy and promoted to captain in 1756. In 1770, while still comptroller, he stood unsuccessfully in the Scarborough by-election with support from the Marquess of Granby.
He married Caroline, 8th Lady Forrester of Corstorphine. Their only child was Anna Maria Cockburne (d.1808), 9th Lady Forrester of Corstorphine.