Lieutenant General Andrew Graham was educated at Eton College and Trinity College Cambridge. Commissioned into the Argyll and Sutherland Highlanders (Princess Louise's) in 1975 he served as a Platoon Commander and Company Commander in the UK, Hong Kong, Northern Ireland, Cyprus, South Georgia and Germany before commanding 1st Battalion The Argyll and Sutherland Highlanders (Princess Louise's) from 1995–1997.
He spent two years in the MOD as Assistant Military Assistant to the Adjutant General before attending the Army Staff College at Camberley in 1988. This was followed by a further tour in the MOD as SO2 MO1 (OE) and then two years as a member of the Directing Staff at the Staff College from 1992–1994.
Following promotion to Colonel, he served as Deputy Assistant Chief of Staff of G3 Command Plans in HQ Land Command in 1997, and commanded 3 Infantry Brigade in Northern Ireland from 1999–2001 before taking over as Director Army RP (Resources and Plans) in the MOD in December 2001. On promotion to Major General, he was deployed as Deputy Commanding General Multi-National Corps to Iraq in 2004.
In October 2004 he took over as Director General of the Army Training & Recruiting Agency (now the Army Recruiting & Training Division). He was appointed Director General of the Defence Academy in May 2008 in the rank of Lieutenant General.