The sway control problem of the pendulum motion of a container hanging on the trolly, which transports containers from a container ship to trucks, is considered in the paper. In the container crane control problem, suppressing the residual swing motion of the container at the end of acceleration or the case of that the unexpected disturbance input exists is main issue. For this problem, in general, the trolley motion control strategy is introduced and applied. But in this paper, we introduce and synthesize a new type of swing motion control system. In this control system, a small auxiliary mass is installed on the spreader. And the actuator reacts against the auxiliary mass, applying intertial control forces to the container to reduce the swing motion in the desired manner. In this paper, we apply the LMI approach and simultaneous optimization design method to design the anti-swing motion control system for the controlled plant. And the simulation result shows that the proposed control strategy is shown to be robust to disturbances like winds and initial sway motion.