System uncertainties and external disturbances are the major causes of the trajectory tracking performance degradation in nonholonomic wheeled mobile robots (NWMRs). In this article, an adaptive fast nonsingular terminal sliding mode dynamic control (AFNTSMDC) method is proposed to provide enhanced robust and finite-time tracking performance for the NWMR. The proposed AFNTSMDC is a systematic design method based upon both the kinematic and dynamic model of the NWMR. The proposed controller has a simple form without singularity issue in the control input, which makes it practically implementable. The finite-time stability of the proposed tracking-error function is also proved using the Lyapunov function. Finally, circular trajectory tracking experiments are conducted to validate the robustness and convergence rate of the proposed AFNTSMDC scheme in comparison with the existing methods including classic kinematic control, robust sliding mode kinematic control, and conventional sliding mode dynamic control in the presence of uncertainties and external disturbances.