The predictive control system using model-based predictive control is a very effective way to optimize the present inputs considering the states and future errors of the reference trajectory, but it has a drawback in that a control input matrix must be repeatedly calculated with a long calculation time at every sampling for minimizing future errors in a predictive interval. In this study, we applied the neural network simulating the predictive control method for the trajectory tracking control of the mobile robot to reduce complex control method and computation time which are the disadvantage of predictive control. In addition, the neural network showed excellent performance by the generalization even for a different reference trajectory. Therefore, The controller is designed by modeling the model-based predictive control gains for the reference trajectory using a neural networks. Through the computer simulation, the proposed control method showed better performance than the general predictive control method.