The purpose of this study is to simplify the tooth flank design of conjugate gears that mesh with involute cylindrical gears on nonparallel axes. It has been clarified and reported that a face gear, which is a gear conjugate to an involute cylindrical gear, has a straight meshing contact line of action in three-dimensional space. The meshing point between the involute cylindrical gear and conjugate gear proceeds at a constant speed along the straight line of action. The straight line of action is continuous and exists as a curved surface called the meshing contact surface of action. In this paper, we discuss the meshing of an involute cylindrical gear and a conjugate gear whose axes are tilted to form an inner bevel-shaped gear. The inner bevel-shaped gear also has a meshing contact surface of action and meshes with the involute cylindrical gear at a constant speed. We demonstrate that it is possible to design the tooth surface of the inner bevel-shaped gear using this meshing contact surface of action.