Martin Van Buren Culver was born around 1834 in Connecticut to Martin and Lucy Culver. His father was a laborer who owned $1,000 of real estate by 1860. He was baptized on December 4, 1840. The family lived in Portland, Connecticut, and by 1850, he was working as a laborer. He moved to Rocky Hill, Connecticut, in the 1850s. By 1860, he was working as a carpenter, and he owned $50 of personal property.
He enlisted in the Union army on August 18, 1862, and he mustered in as a private in Company A of the 16th Connecticut Infantry on August 24. The regiment took part in the Battle of Antietam, the Battle of Fredericksburg, the siege of Suffolk, and the Battle of Plymouth. Confederate forces captured him at Plymouth on April 20, 1864, and imprisoned him at Andersonville. He was paroled on November 30, 1864, and he mustered out on June 24, 1865.
He returned to Portland after the war, and he resumed his work as a carpenter. He helped care for his aging mother until at least 1880. He applied for a federal pension in April 1891 and eventually received one. He died in Portland on April 19, 1907.