We are attempting to develop a new type of vertical MOSFET with SiC/AlGaN heterojunction. Toward the realization of the vertical MOSFET, the control of conduction-band offset is one of the crucial subjects. We investigated the conduction-band offset of 4H-SiC/AlxGa1-xN interface by the first-principles electronic structure calculations. We found that the offset of the interface with 40% Al content becomes almost zero. Therefore, 4H-SiC/Al0.4Ga0.6N interface is one of the most promising candidates for the vertical MOSFET in future power conversion devices.