Micropositioning systems are widely employed in industrial applications. Nonminimum-phase (NMP) is a normal phenomenon in micropositioning system, which leads to a great challenge for control system design. Model predictive control (MPC) is effective in handling the NMP problem. However, the parameter tuning of MPC is quite complicated and time-consuming using traditional methods for motion tracking control implementation. In this paper, an efficient neural networks (NN) model is established to optimize the MPC controller parameters including the prediction horizon, control horizon, and weighting factor. With the developed NN model, the motion tracking process of the micropositioning system is more intelligent and adaptive. The effectiveness of the presented novel NN-MPC control strategy has been verified by conducting extensive simulation studies. Furthermore, the results demonstrate that the NN-MPC scheme has good robustness under model parameter variation and noise condition.