The piezoelectric-actuated stick-slip micro-positioning devices (PASSMDs) have been drawing considerable attention for micro-positioning applications due to their theoretically unlimited motion and good positioning precision. However, the inherent hysteresis of the piezoelectric actuators (PEAs) seriously deteriorates the positioning accuracy of the PASSMDs. In addition, due to the stick-slip actuated principle of PASSMDs, the control of PASSMDs is a challenging job in the literature. This paper proposes a neural network based model predictive control for PASSMDs, which includes the one step control phase and the sub-step control phase. By the proposed method, the hysteresis can be effectively dealt with, which can achieve a relatively accurate positioning performance of PASSMDs. Moreover, to verify the proposed method, a prototype of PASSMDs is developed and experiments are conducted. The experiment results show that the proposed method is an promising way to solve the positioning control of PASSMDs.