In this paper, a grasp force feedback control method of a robot hand attached to a single-link robot arm is proposed, and the usefulness of the grasp force feedback control method is confirmed theoretically and experimentally. The robot hand consists of two permanent-magnet-type stepping motors, reduction gears and plate springs. In the design of the grasp force feedback control system, the start-stop performance without missing steps concerning stepping motors is effectively utilized. For the shock reduction of the robot hand mechanism using stepping motors, the stepping motors should be stopped at a lower pulse rate. Therefore, the grasp force feedback control system is designed to finish the grasp force feedback control at a lower pulse rate of the stepping motors. For this purpose, the control method of the stepping motors using the angular velocity pattern of trapezoidal shape with a constant-velocity time and an estimated finish-time determined by the grasp force feedback control is devised. Then, numerical simulations using the equations of motion of the robot and the grasp force feedback control law have been carried out, and it is ascertained theoretically that the grasping force can be precisely controlled by the present grasp force feedback control method. Furthermore, experiments have been carried out, and the excellent performance of the grasp force feedback control is confirmed experimentally.