In this paper, the constructive modeling procedure of nonholonomic mobile robot system is carried out with the help of controllability Lie algebra used in differential geometry field, and their geometrical properties are also analyzed. And, a new trajectory controller is suggested to guarantee its convergence to reference trajectory. Design procedure of the suggested trajectory controller is back-stepping scheme which was introduced recently in nonlinear control theory. The performance of the proposed trajectory controller is verified via computer simulation. In the simulation the trajectory controller is applied to differentially driven robot system on the assumption that the trajectory planner be given.