Born in 1832 in Ireland, Brennan joined the US Navy from Boston, Massachusetts in May 1861. He initially served as a seaman on the . At the Battle of Forts Jackson and St. Philip near New Orleans on April 24, 1862, he joined the and manned one of that ship's guns through the engagement. His commanding officer stated that he "was the life and soul of the gun's crew." For this action, he was awarded the Medal of Honor a year later on July 10, 1863. Brennan re-enlisted twice more, and was promoted to Acting Master's Mate in November 1863. He deserted from the Navy in August 1864, and the remainder of his life is unknown.