Abraham Graham was a builder and contractor who continued the firm of Abraham Graham & Sons after the death of his father.
He worked for his father in the firm of Abraham Graham & Sons, which he continued after his father's death in 1871. It was likely around this time that his brother Ben established the firm of Ben Graham & Sons.
He married Nancy Bounton on 9 August 1857 and it believed the couple had 13 children.
He represented the West Ward on Huddersfield Country Borough Council from November 1891 for two years. From 1894 until his death he represented the West Ward on the Huddersfield Board of Guardians.
Abraham Graham died aged 66 at his residence of Bankfield House, Bankfield Road, Huddersfield, on 27 May 1899 after an illness of several weeks.