This paper presents a new design of third-order integral terminal sliding mode controller. The control algorithm is designed to reduce the chattering phenomenon and to converge in finite time. The performance of the controller is tested on a piezoelectric nanopositioning system. Experimental result shows that it produces a faster response speed and lower steady-state error in the step response test, and lower tracking error in the sinusoidal wave tracking test as compared with conventional controllers. A series of parametric studies have been conducted to determine the optimal control parameters.