We present a new control method for an active mass damper. Conventionally, a pole assignment method and Linear Quadratic control theory are used for designing the controller of the active mass damper. However, these design methods are not convenient when output of the actuator and movement range of the damper mass is limited, because they cannot restrict any variable directly. Hence, we propose to determine the reference orbit of damper mass first, and control damper mass by a learning controller using the neural network. Our method can keep a mass damper with in a designated range. The performance of our method is better than that of LQ controller in settling time. To show the effectiveness of our method, we apply it to control of an active mass damper for an elastic arm which is a one-degree-of freedom structure. Moreover, we control the experimental system using a neuralnetwork which is learned in a simulation environment.