This study investigated the correction performance of closed-loop control with hysteresis compensation for a piezoelectric unimorph deformable mirror. A closed-loop control algorithm based on the Prandtl-Ishlinskii hysteresis model was established herein. In addition, an adaptive optics test platform based on the Hartmann wavefront sensor was built. The closed-loop correction experiments of static and dynamic aberrations were performed. The experimental results show that for the closed-loop correction of static aberrations, the correction speed of the algorithm with hysteresis compensation is faster than that without compensation. Further, for the dynamic aberrations with an average root-mean-square value of 168 nm, the residual error after correction is reduced from 33 nm before hysteresis compensation to 25 nm after hysteresis compensation. These results prove that the proposed method can be efficiently used in an adaptive optics system with a piezoelectric deformable mirror.