In this paper, we propose a novel mechanism to compensate for gravity and the gripping force in a hand-arm robot. This mechanism compensates for the gravitational torque produced by an object gripped by the hand-arm robot. The gripping force required for the robot hand to prevent the object from dropping is also simultaneously compensated for. This mechanism requires only one actuator placed on the shoulder part of the robot. Therefore, this mechanism can reduce the torque requirement of joint actuators and lower the weight of the robot. The gear ratio of the reduction gears in each robot joint can then also be reduced. These advantages are critical for future robots that perform tasks in unstructured environments and collaborate with humans. We carried out experiments with a 6-DoF robot arm having a 1-DoF gripper to demonstrate the effectiveness of the proposed mechanism.