The nonlinear characteristics of the output displacement of the piezoelectric actuator,such as hysteresis memory characteristics and rate-related characteristics, bring difficulties to the modeling and control of the piezoelectric actuator.This paper proposes a new output displacement control method based on the gated recurrent unit(GRU).The corresponding output displacement experimental platform is set up to verify and analyze the hysteresis of the piezoelectric actuator. The GRU is used to simulate the lagging memory characteristics, and two fully connected layers are used to simulate the rate dependence. The model is an end-to-end system, in which the piezoelectric ceramics and the displacement amplification mechanism are regarded as a whole. The predicted output displacements for different input voltages show that the model has a strong generalization ability for rate-dependent lag.The same cyclic neural network structure is used to construct an inverse model and the experimental test is carried out. The experimental results show that the proposed output displacement control method effectively weakens the nonlinear characteristics of the piezoelectric actuator,which is beneficial for the combination of the linear system control method and the feedforward compensation method.