Sulivan was born in Cawsand, Cornwall on 5 January 1780. By 1786, he was recorded on board HMS Triumph in Portsmouth, then under the command of Samuel Hood, 1st Viscount Hood.[1] He served on several different naval ships until 1793, when he was sent to Mediterranean to take part in French Revolutionary Wars, including being part of the crew of HMS Southampton that captured Utile in 1796, and was promoted to lieutenant the following year.[2]
Sulivan took part in the expedition to Ostend to destroy the Bruges Canal in May 1798 and was present at the bombardment of the Port of Granville in September 1803.[2] In 1807, he took part in the capture of Curaçao, and was promoted to commander for his efforts. in 1813, after a few commands, his ship HMS Woolwich was wrecked in a hurricane, although the crew was saved and Sulivan was acquitted by the subsequent court martial.[2]
On 19 March 1808, Sulivan married Henrietta, daughter of Rear-Admiral Bartholomew James. They had fourteen children, four of whom entered the navy.[4] His son, Bartholomew Sulivan, was a naval officer and hydrographer.[5] He received a CB on 5 June 1815.[2]