Fred Graham was born in Arapuni and grew up in Horahora (Waikato). He trained as a primary school teacher at Ardmore and Canterbury Teachers’ Colleges graduating in 1950. Having specialised in art during his training Graham worked as an Arts Adviser to Māori primary schools in Rotorua and Te Tai Tokerau (Northland); part of Gordon Tovey's promotion of Māori Arts and Crafts in schools. He continued to paint and learning to carve at this time. In Te Tai Tokerau, he worked alongside Ralph Hotere and Muru Walters, who became important friends. His circle would later include artists such as Elizabeth Ellis (née Mountain), Mere Lodge, Paratene Matchitt, Cliff Whiting, and Arnold Manaaki Wilson.
Graham is particularly well-known as a sculptor, and he has undertaken numerous important and large-scale commissions. Combining aspects of Māori artmaking and thinking with Western modernism Graham tended to pare back or abstract customary forms.
In 2017, he received Te Tohu Aroha mō Te Arikinui Dame Te Atairangikaahu (the Exemplary/Supreme Award) in Creative New Zealand’s Te Waka Toi Awards. The following year, he received an Arts Foundation Icon Award Whakamana Hiranga and was named an Officer of the New Zealand Order of Merit.
His son, Brett Graham, is also an acclaimed artist.