Micropositioning systems are widely employed in industrial applications. Nonminimum-phase (NMP) is a normal phenomenon in micropositioning systems, which leads to a great challenge for the control system design. Model predictive control (MPC) is efficient to handle the NMP problem. However, parameter tuning is a time-consuming work for motion tracking control using MPC. In this work, the neural networks (NN) is adopted to provide a functional model for MPC to optimize the prediction horizon and control horizon parameters. It makes the motion tracking process more intelligent and adaptive. The effectiveness of the presented NN-based MPC control scheme is verified by conducting extensive simulation studies.