Moses B. Anderson, SSE was born on September 9, 1928 in Selma, Alabama, and graduated from Knox Academy there in 1949. He was a member of the Society of St. Edmund. Anderson then attended Saint Michael's College in Winooski, Vermont, where he majored in philosophy attaining a B.A. and graduating magna cum laude. From there he moved on to St. Edmund Seminary in Burlington, Vermont. He earned an M.S. in Sociology at St. Michael's College in 1961. He also earned an M.A. in Theology at Xavier University in 1968. During his tenure at Xavier he was a part of a team that formed the Black Catholic Institute.
Anderson was ordained on May 30, 1958. In 1982 he became the first and only African American bishop ordained for the Archdiocese of Detroit. On January 18, 1992, he became the pastor of Precious Blood Parish in Detroit.
He retired in 2003 upon reaching the age of 75; and passed away on January 1, 2013.