This paper presents a discrete-time second-order sliding mode control scheme dedicated to precision motion control of a nanopositioning stage driven by piezoelectric actuators. Unlike conventional discrete-time sliding mode control (DSMC), the second-order DSMC allows the elimination of chattering phenomenon. A stability analysis of the proposed second-order DSMC control strategy is carried out. Based on the plant model of the system, the controller parameters are assigned. Comparative studies are conducted using the reported scheme and conventional proportional-integral-derivative (PID) control. Results show that the second-order DSMC scheme is superior to PID control in terms of motion tracking accuracy. In addition, the control scheme is easy to realize, and it can be extended to other types of systems as well.