Aiming at the nonlinear characteristics of rate-dependent hysteresis of piezoelectric stack actuators, a BP neural network rate-dependent hysteresis modeling method based on the Asymmetric unilateral backlash (aubacklash) operator is proposed in this paper. Firstly, an improved aubacklash operator is proposed to improve the residual displacement at the origin and strict center-symmetry of the backlash operator of Prandtl-Ishlinskii (PI) model. Secondly, the rate-dependent memory characteristics of hysteresis of piezoelectric stack actuator are analyzed, and a rate-dependent BP neural network hysteresis model is proposed. Finally, the accuracy evaluation system of hysterectomy modeling is set up, the parameters of aubacklash operator model are identified by Levenberg-Marquardt(L-M) algorithm, and the optimal structural parameters of BP neural network model are determined. The experimental results show that the mean square error of BP neural network model is reduced by 70.90%~89.98% and the relative error is reduced by 70.69%~89.84% compared with the traditional PI model at high and low single frequency and mixed frequency, which verifies the accuracy and frequency adaptability of the model.