The deformable aspheric polishing lap based on Piezoelectric(PZT) actuator can change the lap surface continuously to fit the surface of middle aperture aspheric optical mirrors at any location. In this paper,a 100 mm diameter and deformable aspheric polishing lap consisting of 19 PZT actuators was designed and manufactured to polish a Φ350 mm hyperboloid mirror in k＝－1.112 155, R=840 mm. In order to analyze the influence of PZT actuator hysteresis on surface error, the output characteristic of each PZT actuator was measured and the mathematical model of displacement output of each PZT actuator was established by means of Radial Basis Function(RBF) neural network. By finite element method, the surface errors of the deformable aspheric polishing lap were calculated before and after PZT actuator hysteresis compensation. The results show that the surface residual error and RMS are 1.910 μm and 0.342 μm respectively. By PZT actuator hysteresis compensation, the surface error of the deformable aspheric polishing lap reduces by 82%.