Colonel Graham Thompson was born in Melbourne on 2 January 1921. He enlisted in the Australian Imperial Forces (AIF) in May 1941 and was commissioned in 1942. Initially he served with the 2/6th Battalion, the 2/14th Battalion and 14th Infantry Battalion in Victoria. In August 1942 he joined the 14/32nd Infantry Battalion in Western Australia and served with this battalion in New Guinea and New Britain from 1943 to 1945 as a platoon commander, assistant adjutant and adjutant.

He left the Army for a short period and on re-joining in August 1948 he served as Adjutant of the Army Apprentices School and then as Adjutant of 45th Infantry Battalion at Arncliff in NSW. He attended the Army Staff College in 1953 after which he was posted to HQ 28 British Commonwealth Brigade in Korea. This was followed by staff and training appointments including two postings as an instructor on Tactics Wing at the School of Infantry at Seymour, Vic. During this time he qualified as a parachutist. In 1961-63 he was posted to the UK School of Infantry at Warminster as an Instructor in Tactics.

In April 1963 Colonel Thompson was posted as a company commander with 1st Battalion Royal Australian Regiment (1RAR). After staff postings as a Lieutenant Colonel in Army Headquarters (AHQ) Canberra and HQ Communication Zone in Sydney, he served in South Vietnam in 1968-69 with the Amenities & Welfare Unit, HQ AFV. He then became Commanding Officer of the Army Apprentices School at Balcombe, Victoria. Colonel Thompson was Commanding Officer of 5RAR from 13 July to 13 September 1970 at Holsworthy NSW. He retired from the Army in January 1971 and granted the title of Colonel.