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