Mossell married Mary Louisa Tanner in Philadelphia around 1890. They had three children. Aaron Albert Tanner III (1893-1959) became a pharmacist in Philadelphia. Elizabeth Mossell Anderson (1894–1975) became Dean of Women at Virginia State College and later at Wilberforce University in Ohio. Sadie Tanner Mossell (1898–1985), also graduated from Penn and served as an editor of the Law Review., became a practicing lawyer, Assistant City Solicitor and activist on civil rights issues
