This paper reports on the design and verification of a new output feedback-based discrete-time terminal sliding mode control (DTSMC) scheme, which is applied to achieve precision motion control of a piezoelectric nanopositioning system by overcoming the unmolded nonlinearity and external disturbance. The controller is easy to implement because it does not require a hysteresis model and a state observer. It can offer a precise tracking without chattering phenomenon. The stability of the control system is proved analytically and the effectiveness of the control scheme is demonstrated through experimental studies. Experimental results show that the nonlinear DTSMC robust control is superior to conventional linear discrete sliding mode control in motion tracking application.