This paper proposes a dual-loop control strategy to address the trajectory tracking problem of differential wheeled mobile robots (WMRs). First, the kinematic model of the WMR is established, and the dynamic model including the actuators is derived. To tackle the issue of y-axis direction divergence in existing methods, a predefined-time velocity control law based on intermediate variables is proposed. By introducing the y-axis error term into the angular velocity control, the ability to rapidly track the target trajectory is enhanced, providing a reliable velocity tracking target for the dynamic controller. Furthermore, a predefined-time nonsingular fast terminal sliding mode controller is designed, which combines a nonsingular fast terminal sliding surface with predefined-time stability theory to overcome the singularity problem in existing approaches, achieving fast and accurate tracking of velocity errors. Additionally, to improve the system’s disturbance rejection capability, a nonlinear extended state observer (NESO) is proposed to estimate external disturbances and provide feedforward compensation to the dynamic controller. Experimental results demonstrate that the proposed strategy outperforms existing methods in terms of trajectory tracking accuracy and robustness, providing an effective solution for the high-performance control of WMRs.