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Control of structure responses induced by earthquake excitations is chiefly considered in many researches due to its heavy damages and vital harms in many cases. In this paper, a control system is developed to attenuate the vertical responses of a 5-story structure. A passive control device is proposed and 6-DOF structural model is developed. Neural Network method is employed to specify the optimum values of the controller parameters. The simulation of multi-DOF structure model is performed for several set of assumed values of the controller parameters to provide adequate data to make a trained network. The trained network is used to specify proposed controller parameters. Finally, the control system based on the Neural Network method is used and its effect on the improvement of the structure responses is evaluated.