Martin H. Anderson was born on March 7, 1844, in Indiana to William and Susan Anderson. His father was a plasterer who owned $50 of personal property by 1860. He grew up and attended school in Indianapolis, Indiana.
He enlisted in the Union army on August 19, 1863, and he mustered in as a private in Company D of the 117th Indiana Infantry later that day. He mustered out on February 25, 1864. He returned to the Union army a year later, mustering in as a private in Company B of the 145th Indiana Infantry on January 17, 1865. He mustered out on January 21, 1866.
Anderson married America Jane Ritter on July 7, 1864, and they had at least three children: Howard, born around 1865; David, born around 1867; Nora, born around 1869. They lived in Jackson, Indiana, and he worked as a farm laborer. He applied for a federal pension in April 1880 and eventually secured one.
His wife died by the early 1880s, and Anderson married Margaret Huff on August 29, 1883. They had at least three children: Harry, born around 1884; Peter, born around 1886; and Darthia, born around 1896. They settled in Shawswick, Indiana, in the late 1800s, and Anderson worked as a laborer and a carpenter. They moved to Bedford, Indiana, in the 1910s. He died of carcinoma there on July 12, 1923.