The robust and precise control of piezoelectric stages is quite challenging due to the existence of strong hysteresis nonlinearity. In this paper, the dynamics of a piezoelectric stage is identified as a second-order linear system preceded by an input hysteresis characterized by the Prandtl-Ishlinskii (PI) model. Then, a control strategy based on the uncertainty and disturbance estimator (UDE) is developed to mitigate the effect of hysteresis nonlinearity and improve the performance of the positioning control of the piezoelectric stage, without the detailed model of the hysteresis except the slope information of the PI hysteresis asymptotes. Moreover, the stability analysis of the closed-loop system with the UDE-based controller is provided. Extensive experimental studies are carried out on a Physik Instrumente P-753.31c piezoelectric stage to demonstrate that the UDE-based controller can achieve excellent performance in trajectory tracking and disturbance rejection, compared to the proportional-integral-derivative (PID) controller and a disturbance-observer-based controller.