To eliminate the position deviation and direction error of trajectory tracking for the automated guided vehicle (AGV) wheeled parking robots in underground garages, a sliding mode controller is designed with a Lyapunov direct method and an improved fast stationary power approach law. Firstly, a kinematic model of the AGV wheeled parking robot in the global coordinate system is established. In order to make the AGV wheeled parking robots transfer from the deviation state to the sliding mode switching surface quickly and track the given reference trajectory stably, a novel fast stationary power approach law is proposed. Then, the Lyapunov direct method and the fast stationary power approach law are used to design the sliding mode controller. Finally, MATLAB software is employed to conduct the simulation tests of trajectory tracking. The simulation results obtained by adopting the fast stationary power approach law and traditional power approach law are compared. The compared results show that the former performs better in tracking the desired trajectories. The effectiveness of the designed controller is verified through simulation tests.