Abstract: A robot kinematic model with two independent driven wheel angular velocities as control inputs was obtained through the observation and analysis of trajectory tracking problem for nonholonomic mobile robot whose mass centers are not coincidental with the geometrical centers.Based on the backstepping control algorithm, a switch function for variable structure control is designed and a sliding-mode tracking control law with global asymptotically stability is proposed for these systems with the known wheel radius and the distance between the two driving wheels.In order to deal with the circumstance with the unknown two parameters above, an adaptive sliding-mode tracking control law is proposed by employing the adaptive method to estimate the unknown parameters.This method simplifies the controller design and is applicable to the trajectory tracking control of the mobile robot.The global asymptotically stability of the closed loop system is guaranteed by Lyapunov direct method.Simulation results are provided to demonstrate the effectiveness and correctness of the proposed method.