Stephen Graham was born in Kirkby, Lancashire, on 3 August 1973. He was brought up by his mother, a social worker, and his stepfather, a mechanic who later became a paediatric nurse. He maintained a good relationship with his biological father. He had a Swedish grandmother and Jamaican grandfather, and has discussed his experience being a light-skinned multiracial person, as he has brothers who have much darker skin.
He attended Overdale Primary School in Kirkby, where he was encouraged to pursue an acting career at the age of eight by local actor Andrew Schofield, who had seen him perform as Jim Hawkins in a school production of Treasure Island. He then continued his education at Ruffwood Comprehensive and was subsequently introduced to Liverpool's Everyman Theatre at the age of 14, later going on to train at the Rose Bruford College of Theatre & Performance.