He was the author of Aircraft Carriers at War: A Personal Retrospective of Korea, Vietnam, and the Soviet Confrontation published in 2007 by the Naval Institute Press.

He graduated from Saint James School, Maryland in 1939 and was appointed to the United States Naval Academy in that year as a member of the Class of 1943.

Holloway graduated from the Naval Academy in June 1942 as a member of the first three-year class accelerated by World War II.

He was gunnery officer of the destroyer Bennion, which at the Battle of Surigao Strait took part in a night torpedo attack which sank the Japanese battleship Yamashiro, assisted in the destruction of the destroyer Asagumo, attacked the cruiser Mogami with torpedoes, and then the following day shot down two Japanese Zeroes at short range.

He made two carrier tours to Korea, flying Grumman F9F-2 Panther jets on combat missions against the North Korean and Chinese Communists.

Holloway took command of the Seventh Fleet in 1972 during the Vietnam War, and personally led a cruiser-destroyer gunfire strike force during the Battle of Haiphong Harbor.

During Operation Linebacker II, he directed the massive carrier strikes against Hanoi, which were a part of the intensive joint air effort which led to the Vietnam cease-fire in 1973.

As Chief of Naval Operations (CNO) from 1974 to 1978, Holloway was a member of the Joint Chiefs of Staff (JCS), and served as CNO during the evacuation of Cyprus; the rescue of the merchant ship SS Mayaguez and its crew, and punitive strike operations against the Cambodian forces involved in its seizure; the evacuation of U.S. nationals from Lebanon; and the Korean demilitarized zone incident in August 1976, which led to an ultimatum and an armed standoff between the Allied and North Korean armies before the North Koreans backed down.

After retiring from the navy in 1978, Holloway was a consultant to Paine Webber, Inc. and served until 1988 as president of the Council of American-Flag Ship Operators, a national association of U.S. merchant marine companies.

Holloway was chairman of the Academic Advisory Board of the United States Naval Academy, chairman of the Association of Naval Aviation, a director of the Olmsted Foundation, a trustee of the George C. Marshall Foundation, served on the Board of Visitors and Governors of St. John's College and served in a presidential appointment as US Representative to the South Pacific Commission.