The trajectory tracking control problem of nonholonomic mobile robots with a fixed camera is investigated based on a kind of nonholonomic robot kinematics model and chained transformations, when the center of mass and geometric center coincide. Firstly, a robot-camera visual servoing kinematic tracking error model is proposed by utilizing the pin-hole camera model. Then, based on this model, an adaptive torque tracking controller involving a kind of dynamic feedback parameters is designed by using the Lyapunov direct method and backstepping technique, which is different from the previous treatment method. The controller realizes the global asymptotic trajectories tracking of the dynamic system. The stability of the closed-loop system and the boundedness of the estimated parameters are strictly proved using the Lyapunov method. Finally, Matlab simulation is carried out to verify the effectiveness of the proposed controller.