During World War II, he was executive officer of Fighter Squadron 1 operating off the carrier USS Yorktown (CV-10) and commanding officer of the Air Group 35 aboard the aircraft carrier USS Chenango (CVE-28) in the Pacific.
During the Korean War, he was the commanding officer of naval air training at NAS Pensacola and the air officer on the USS Coral Sea (CV-43).
His first sea command was aboard the USS Suribachi (AE-21).
In 1962–1963, Moore was the eighth commanding officer of USS Saratoga (CV-60).
Late in his career during the Vietnam War, he was Chief of Staff of the Naval Air Training Command at Naval Air Station Pensacola from October 1965 to July 1969.