We present an exact solution on the ground state of a one-dimensional orbitally degenerate Hubbard model in the case of strong coupling, and the phase diagram in terms of electron filling and relevant parameters. The ground state is nondegenerate apart for spin SU(2) symmetry and a fully saturated and metallic ferromagnet except the case of the quarter filling, at which a ferromagnetic Mott insulator transition occurs. The phase diagram shows coexistence of ferromagnetism and spin-triplet pairing superconductivity when the Hund coupling is sufficiently larger. A mechanism for spin-triplet pairing superconductivity and its possible relevance to the quasi-one-dimensional organic superconductor are proposed.published_or_final_versio
