A discrete-time tracking differentiator (TD) based on a time criterion is presented. Its control law is derived by comparing the time that the initial state is driven to the switching curve or the origin with the sampling period. The advantages of this TD include faster signal-tracking, better noise filtering and derivative extraction. Simulation results show that this TD has smaller errors in signal-tracking and derivative extraction compared with the existing differentiators. Experiments are carried out on the gap sensor of the suspension control system in a magnetic-levitation (maglev) train to demonstrate that the proposed TD can obtain an effective velocity signal from the gap sensor when the accelerometer fails.