A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two electrons. The features of ground state and excited states for repulsive coupling are shown. For finite N number of electrons, the configurations of quantum numbers are given explicitly and the spectra of excitations are obtained by solving the Bethe-ansatz equation numerically. For infinite N, the ground state and various kinds of low-lying excitations are obtained on the basis of thermodynamics limit