This paper presents the design, analysis, and verification of a new output-based digital integral terminal sliding mode predictive control (DITSMPC) scheme, which is dedicated to precision motion control of a piezoelectric-driven positioning system. Unlike existing similar work, the controller is easy to implement because it does not require a hysteresis model and a state observer. Moreover, it is chattering free and is capable of delivering an O(T2) output error. The stability of the control system is demonstrated in theory. It is found that the model predictive control (MPC) enables a further improvement on the tracking accuracy in comparison with the digital integral terminal sliding mode control (DITSMC) schemes. The effectiveness of the proposed control strategy is confirmed through experimental investigations. Experimental results show that the DITSMPC control is superior to DITSMC and robust DITSMC (RDITSMC) schemes in motion tracking application, which is enabled by a well robustness property in the presence of model disturbances.