This paper presents the design and testing of a novel continuous third-order integral terminal sliding mode control (3-ITSMC) strategy dedicated to motion tracking control of a piezoelectric-driven nanopositioning system. In comparison with the available sliding mode controllers, the significant improvement of the proposed controller lies in the fact that it completely eliminates the chattering effect, achieves a finite-time convergence, and produces a higher sliding mode precision. The model uncertainty involving the hysteresis effect is estimated by the perturbation estimation technique. Higher order derivatives of the position are generated by using a robust exact differentiator. Based on an integral terminal type of sliding surface, a third-order sliding mode precision is obtained by resorting to the third-order supertwisting algorithm. The convergence and stability have been proved in theory. The performance improvement of the developed controller versus the conventional second-order and third-order sliding mode controllers is validated by carrying out both simulation and experimental studies. Results demonstrate that the proposed 3-ITSMC controller provides quicker transient response speed and smaller steady-state error for the piezoelectric nanopositioning system along with a better robustness against model uncertainty and external disturbance.