In structure design, a radical conversion from the traditional specifications design method to the performance design method is being considered. Considering performance design from the viewpoint of the seismic performance, the problem of response control of the structure for the predicted earthquakes becomes an important theme. The accurate estimation of the response of the structure for the predicted earthquakes is necessary for the response control of the structure. There are many studies for the response estimation of the structures (Kinugasa, 1996), (Nakamura, 1998). This paper reports that the response displacement based on the energy theory for the Reinforced Concrete (RC) structures can be estimated accurately by introducing the hysteresis energy coefficient (CE). But, it is difficult to determine CE theoretically, because CE has complicated functions. However, a neural network is effective for identifying such a function. In this paper, CE is determined by a neural network's training.