A sliding mode trajectory tracking control with fast stationary power reaching law was proposed to address the problem of position and attitude deviation in the trajectory tracking process of automated guided vehicle (AGV) wheeled parking robots applied in underground garages. First, a kinematic model was established under the coordinate system of the parking robot, and the kinematic model of the parking robot under the global coordinate system was obtained through the transformation relationship between the global coordinate system and the robot coordinate system. Then, the Lyapunov direct method was used to design the sliding mode switching function, and a fast stationary power reaching law was adopted to quickly reach the sliding mode switching surface of the parking AGV from the deviation state, enabling the AGV parking robot to quickly and stably track the given reference trajectory. Finally, simulation experiments were conducted using MATLAB, and the simulation results verified the feasibility and effectiveness of the proposed method.