Benjamin W. Frost was born around 1834 in Massachusetts to Richard and Esther Frost. He grew up in Lowell, Massachusetts, and by 1860, he was earning a living as a clerk. He married Amelia A. McDowell on April 16, 1861, and they had at least six children: Josephine, born around 1862; Helen, born around 1865; Katie, born around 1870; Martha, born around 1874; Elizabeth, born around 1877; and Harry, born around 1879.
He enlisted in the Union army on April 16, 1861, and he mustered in as a sergeant in Company H of the 6th Massachusetts Infantry on April 22. He mustered out on August 2, 1861. He returned to the Union army soon afterwards, mustering in as a 1st lieutenant in Company H of the 26th Massachusetts Infantry on October 18, 1861. He was promoted to captain on February 7, 1862, and he mustered out on November 4, 1864.
Frost returned to Massachusetts after the war, and he earned a living as a wool merchant. He moved to Brooklyn, New York, in the late 1860s, then to Jersey City, New Jersey, in the 1870s. He applied for a federal pension in June 1888 and eventually secured one. By 1900, he was living in New York City. He died around 1914.