This paper proposes a dynamic feedback controller for a differential drive-wheeled mobile robot (DDWMR) to achieve the motion trajectory tracking with minor errors. The kinematic and dynamic model of DDWMR is presented. Based on that model, the dynamic feedback controller is designed. The Lyapunov stability method derives an adaptive gain, ensuring the system's dynamic asymptotic stability. In the simulation problem, the DDWMR's inertial coefficients are resoluted by the Solidworks software's Mass Properties tool. The simulation results have verified that errors in the x-direction and y-direction are within 3.25 mm and 2.55 mm, while the pose error is within 0.022 rad. The research results have significant implications for the trajectory tracking of DDWMR in the industry.