This paper develops a disturbance observer-based discrete-time sliding mode control (DOB-DSMC) method to address the trajectory tracking problem for nonholonomic robots subject to disturbances. Firstly, a reduced-dimensional tracking error system is derived to overcome the disadvantage of the underactuated robot system. In the light of reduced-dimensional system, a disturbance observer is studied to estimate and compensate for disturbances. Then, inspired by the continuous terminal sliding mode surface, a novel discrete-time terminal sliding surface is designed. Further, the arctangent function is inducted to improve the tracking accuracy and attenuate the chattering phenomenon. Moreover, the asymptotic stability of system is proved via the Lyapunov method. Finally, the effectiveness of the exploited algorithm is verified by a numerical simulation.