Henry Murray was born around 1845 in Charlottesville, Virginia, and worked as a laborer before the war. On June 1, 1864, he enlisted in the Union navy for three years at Skipwith’s Landing in Issaquena County, Mississippi. Officials listed his race as "negro" and gave him the rating of landsman. It is not clear if he was a slave prior to enlistment. He first saw service onboard the USS Laurel, a screw steamer that supported both army and navy operations and attempted to cut western Confederate supply lines to the Eastern Theater. The ship never engaged in naval combat, engaging mainly in patrol and reconnaissance duty on the Mississippi River.

Sometime before December 31, Murray transferred to the USS Louisville, where he served alongside John Edwards and David Linton, two other Albemarle-born Black sailors. The War Department transferred the Louisville, an ironclad centerwheel gunboat, to the navy on October 1, 1862. By the time Murray joined her crew, she had returned to patrol and army support duty, and she remained there until being decommission on July 21, 1865. Murray's last muster roll is dated July 18, 1865, which is probably about the time he left the navy. He never filed a pension, and nothing is known about his post-war life.