The aim of the paper is trajectory tracking control of a non-holonomic mobile robot whose centroid doesn’t coincide to its rotation center in the middle of connecting axle of driving wheels. The nonholonomic dynamic model of the Wheeled Mobile Robot (WMR) is developed in global Cartesian coordinates where the WMR’s forward and angular velocities are used as internal state variables. In order to include the effects of parameter uncertainties, measurement noises and other anomalies in the WMR system, a bounded perturbation vector is embedded to the developed dynamical model. Through defining the control inputs by computed torque method, a Dynamic Sliding Mode Controller (DSMC) is proposed to stabilize the sliding surfaces. Based on the proposed robust control system, the effect of uncertainties and noises in the robot performance is attenuated. By use of the WMR forward and angular velocities as internal state variables in the dynamic modeling, the developed model is relatively simple and mainly independent of the robot states. This makes the dynamical model more robust against measurement errors. Design of the DSMC based on such a model leads to perfect trajectory tracking and compensation for initial off-tracks even in the presence of disturbances and modeling uncertainties.