This paper presents the design of a new continuous third-order sliding mode robust control scheme dedicated to trajectory tracking control of a piezoelectric-actuated motion system. One uniqueness of the developed controller is that it achieves inherent chattering-free control action with finite-time convergence. The model uncertainty including the hysteresis effect is estimated by perturbation estimation technique. Higher order derivatives of the position are estimated by using a robust sliding mode observer. A novel third-order sliding mode control (TOSMC) is devised and its stability is proven based on Lyapunov analysis. The performance of the developed controller is validated and compared by carrying out real-time experimental studies. Results demonstrate remarkable robust tracking performance of the controller over existing second-order sliding mode control and TOSMC in terms of steady-state accuracy and robustness property with equivalent control effort.