A posture control method for a hopping robot has been proposed in this paper. The control of the hopping robot is decomposed into two types of controls: the posture control that maintains the horizontal speed and the angles of a body and a leg, and the jumping control that keeps the jumping height. The posture motion of the hopping robot is approximated by a set of two linear continuous time systems for stance and flight modes, and two mode transition maps at touchdown and lift-off. We have shown that the posture of the robot can be stabilized by selecting a set of state feedback laws via numerically solving a minimax problem. Simulation results showed that the whole system is stabilized by the proposed control law, provided that the jumping heights maintained constant appropriately. We have also shown by simulation that the obtained feedback law provides smaller stabilizing inputs compared to one obtained by the Raibert's method. We have developed an actual one-legged hopping robot, and have shown that the robot can be stabilized and run at the specified speed by the proposed method and a simple jumping control.