First-principles calculations of abrupt SiO2/4H-SiC and 6H-SiC(0001) interfaces have been performed. The calculated interface states, which originate from dangling bonds of interface Si atoms, lie 1.8 eV above the valence band edge of the SiO2/4H-SiC and the SiO2/6H-SiC interfaces. These states vanish when Si dangling bonds are saturated with hydrogen atoms. In the carbon cluster model, interface states appear not only at the conduction band edge but also at the valence band edge.