Graham was born in 1812 at Frogmore in Berkshire,[5] England, and christened at St George's Chapel, Windsor Castle, that year.

[6][5] Graham accompanied the staff of Lieutenant Governor William Hobson to New Zealand and was present at the signing of the Treaty of Waitangi in February 1840.

[7] Back in Sydney, in May he received an order to return to New Zealand "to superintend the erection and take charge of the military and convict buildings there".

With no definite guidance from Lieutenant Colonel George Barney, CRE, in Sydney, and left to improvise, Lugard, Graham and the artificers constructed a temporary rustic loop-holed barrack with attached rear cookhouse of saplings; two roomed officer’s quarter; separate officer’s kitchen; privies; and partially erected a wooden barrack house from Sydney, at Russell/Okiato within four months.

The Flagstaff War in the Bay of Islands in 1845–1846 put a scare to the population of Auckland, and Graham supervised the enlargement of the Albert Barracks overlooking the town.