In general, the swing motion of the crane is controlled and suppressed by activating the trolley motion. In this paper, we suggest a new type of anti-sway control system of the crane. In the proposed control system, a small auxiliary mass(moving-mass) is installed on the spreader and the swing motion is controlled by moving the auxiliary mass. The actuator reaction against the auxiliary mass applies inertial control forces to the container in order to reduce the swing motion in the desired manner. In this paper, we apply the $H_{infty}$ based control technique to the anti-sway control system design problem. And the experimental result shows that the proposed control system is useful and robust to disturbances like winds and initial sway motion.