We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction
U<0 using the density-matrix renormalization-group method as well as perturbation theory. We find that the ground state is a charge-density-wave state with long-range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap, which is the same as the four-particle excitation gap, is a nonmonotonic function of
U, while the spin gap and others increase with increasing $\ensuremath{\mid}U\ensuremath{\mid}$ and have linear asymptotic behaviors.