A quadrupedal water runner robot inspired by the basilisk lizard has previously demonstrated the capability of water surface locomotion. Since the robot is aimed for the amphibious locomotion, a compatible design on both ground and water surface is discussed in this paper. A compliant footpad which can transfer elastic energy to propulsive momentum is introduced and modeled using a pseudo-rigid-body model. Dynamic modeling of the footpad and the robot provides a criterion of efficient ground locomotion. For the water surface locomotion, drag force can be reduced by compliance of the footpad. The optimized design taking into account two locomotions is studied and analyzed for stability using the Poincaré map.