It is aimed to minimize the structure response against the earth vibration by the use of the open loop control system. In such a control, only one predicting neural network is utilized, which estimates only the earth vibration. The neural network is instructed by some recorded acceleration data, and it is able to predict the acceleration variation for the subsequent step. The control force is equal to the product of the mass of each story to its next step acceleration. This control system leads to the approximate minimum response. Moreover, to guarantee the system stability, a linear controller is added to the system. The resulted mixed control system can assure the system stability and also has better performance. Finally, the effect of the structural mass variation on the control system is investigated. The findings show that the effect of the structural mass variation on the mixed control system is smaller than the one by the predicting neural network.