We suggest a new type of swing motion control system for a crane system in which a small auxiliary mass is installed on the spreader. The actuator reacting against the auxiliary mass applies inertial control forces to the spreader of the container crane to reduce the swing motion in the desired manner. In this paper, as the basic and first step, we apply the $H_{infty}$ control approach to anti-sway control system design problem. And, it will be shown that the proposed control strategy is useful and it can be easily applicable to the real world. So, in this study, we investigate usefulness of the proposed anti-sway system and evaluate system performance through simulation and experimental studies.