The work aims to solve the trajectory tracking problem of a class of under-actuated handling robots when the centroid and the center are not coincident. The kinematics and dynamics models of under-actuated robot with nonholonomic constraints were established. Based on the back-stepping control theory, a new virtual feedback was constructed and a tracking controller was designed. At the same time, the adaptive technique was introduced to correct the parameters of the tracking controller with uncertainties. The global stability of the control system was proved by Lyapunov theory. The simulation results showed that the actual trajectory of the under-actuated handling robot could quickly follow the desired path. The feasibility and effectiveness of the tracking controller based on back-stepping method were verified. The designed controller can make the handling robot achieve good trajectory tracking results, and ensure the adaptivity of the controller.