Nonlinear piezoelectric hysteresis reduces the openloop control precision and closedloop operation bandwidth of the piezoelectric deformable mirror (DM), which limits its applications in adaptive optics (AO) system. In order to overcome the hysteresis influence of the piezoelectric deformable mirror, the PI hysteresis model was adopted to describe the nonlinear hysteresis behavior of a unimorph piezoelectric deformable mirror and achieve the high precision openloop control of the unimorph piezoelectric deformable mirror. Firstly, the mathematical model of PI hysteresis was established. The least square method was used to identify the weight value of the PI hysteresis model. The weight value and threshold value of the PI inverse model were calculated. The control voltage of the unimorph piezoelectric deformable mirror after hysteresis elimination was obtained. Then, an adaptive optical test platform based on Hartmann wavefront sensor was built. The openloop control experiment of the defocus wavefront using a ring actuator of the unimorph piezoelectric deformable mirror was carried out. The experiment results show that the voltagedeformation hysteresis of the unimorph piezoelectric deformable mirror is reduced from 9.3% to 1.2% after hysteresis elimination. The openloop reconstruction accuracy of the defocus wavefront is improved by more than 70%, which proves that the proposed PI hysteresis model can be effectively applied in the openloop control of the unimorph piezoelectric deformable mirror.