This paper presents the design of a novel second-order discrete-time terminal sliding-mode control (2-DTSMC) strategy and its application to motion tracking control of a piezoelectric nanopositioning system, which possesses a high-order plant model. The 2-DTSMC strategy is established based on the output feedback only, which eliminates the use of a state observer and facilitates an easy realization. Theoretical analysis proves that the quasi-sliding mode is reached in finite time along with high accuracy of the output tracking. The effectiveness of the proposed control scheme is validated through comparative investigations. Experimental results show that the 2-DTSMC strategy is superior to traditional discrete-time sliding-mode control (DSMC), second-order DSMC, and DTSMC algorithms in terms of motion tracking accuracy, which demonstrates the efficiency of the reported 2-DTSMC scheme with a second-order nonlinear sliding surface. © 1982-2012 IEEE.