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Abstract In order to realize the automation of transport equipment, according to the automatic guided vehicle (AGV) kinematics model, the trajectory tracking control of AGV with front wheel steering and rear wheel drive is studied. Lyapunov function is used to ensure the global stability of the system. Time-varying state feedback method based on integral backstepping is adopted, introducing virtual feedback, a trajectory tracking controller for AGV with nonholonomic constraints is proposed. In order to ensure the smooth motion of AGV, the speed and acceleration limited strategy of AGV is introduced into the controller. Simulation results show that the algorithm is fast, accurate and globally stable for different paths.