Piezoelectric actuators have the characteristics of fast response, large mass ratio, high rigidity, etc., and have been widely used in the field of nanotechnology. As a kind of inherent nonlinear characteristic, hysteresis characteristic greatly affects the performance of hysteresis control. This paper proposes a nonlinear model predictive control (NMPC) method to solve the displacement tracking problem of piezoelectric actuators. First, the RBF neural network is used to realize the "external input nonlinear autoregressive moving average" (NARMAX) model of the piezoelectric actuator; secondly, the NMPC principle is used to transform the tracking control problem into an optimization problem, and then the gradient descent algorithm is used to solve it. In order to verify the effectiveness of the proposed modeling and control methods, MATLAB and COMSOL simulation experiments were carried out. The results show that the proposed RBF prediction model has satisfactory accuracy, the maximum absolute error between the expected displacement and the actual displacement obtained by the NMPC method tracking is 0.016um, and the average absolute error is 0.0121um, which has high accuracy.