The tilt mirrors and deformable mirrors in adaptive optics system are usually using piezoelectric ceramic actuators for precise displacement, however, piezoelectric ceramic actuators own obviously nonlinear hysteresis effect which affects the positioning performance of the system. In order to compensate the hysteresis, there is a need to model hysteresis effects. In this paper, hysteresis operator is introduced and using Bayesian regularization training algorithm to train BP neural network to construct hysteresis model of piezoelectric ceramic actuator, an experimental study was conducted on a piezoelectric actuator developed by Institute of Optics and Electronics, Chinese Academy of Sciences. The final experimental results show that the hysteresis model of piezoelectric ceramic actuators constructed by BP neural network has more accurate identification capability. The relative error of the positive model is 0.0127 and the relative error of the inverse model is 0.014. The nonlinearity of the piezoelectric Displacement/μm actuators has been reduced from 14.6% to 1.43%.