Abiel A. Livermore was born around 1838 in Wilton, New Hampshire, to Jonathan and Dorcas Livermore. His father was a farmer who owned $1,200 of real estate and $400 of personal property by 1860. He grew up and attended school in Wilton, and by 1860, he was working as a farmer and miller. He supported the Republican Party.
He enlisted in the Union army on October 26, 1861, and he mustered in as a private in Company B of the 8th New Hampshire Infantry on December 20, 1861. He was promoted to corporal on March 20, 1863. He died of disease near Port Hudson, Louisiana, on July 3, 1863.