By using scattering-theoretical method, we have calculated the surface-band structure of ideal and （２×１） reconstructed β-SiC(100) surface, and the lay-, atom-and orbital-resolved densities of states. The results show that the major effects of reconstruction occur in the band-gap energy region, and the reconstructed Si and C terminated surfaces are semiconducting. Our calculated surface-band structure are in good agreement with experiments. According to the bonding states and localized state densities of two dimerized atoms, the dimeric symmetry of Si atoms and the dimeric asymmetry of C atoms have qualitatively been explained.