This paper presents a new trajectory tracking control algorithm to uncertain mobile robot with nonholonomic constraints. This algorithm is based on the non-singular terminal sliding mode technique, which can eliminate the singularity problem caused by conventional terminal sliding mode control. The system state vector is designed using backstepping method, this method breaks down nonlinear systems into low dimensional systems and simplifies the controller design. By combining Lyapunov method, it is proved that under this control law, the pose errors converge to zero, the mobile robot can track the desired trajectory when the desired velocity satisfies some assumptions. Simulation results validate the theoretical analysis.