Born in Huntsville, AL in 1866 Moore won his B.A. (1889) and his M.A. (1893) from Fisk University in Nashville. In 1896 he earned the one of the first doctorates awarded to a black person in the United States. He did this at the University of Pennsylvania with a dissertation entitled "The Stage in Sophocles." He taught Latin at Howard University until 1899 when he became an administrator there.