Albert Franklin Fish was born on December 29, 1849, in Lowell, Massachusetts, to John B. Fish and Mary H. Barrett. His father was an iron founder. The family lived in Lowell until the 1850s, when they moved to Manchester, New Hampshire. They moved to Cambridge, Massachusetts, in the 1860s, and by 1870, Fish was working as an iron moulder.
His father died on October 25, 1875, and he remained in his mother’s household until at least 1880. He married Anna E. Bangs on September 5, 1898. They lived in Cambridge, and he helped care for his mother as she aged. By 1910, they were living in Medford, Massachusetts. His wife died in 1920. He died of a heart attach on August 12, 1934, in Boston, Massachusetts, while attending church.