Aiming at the trajectory tracking control problem of four-Mecanum-wheel AGV (Automatic Guided Vehicle), this study designs a controller named MPC+ELM-SMC, which connects model prediction control and adaptive sliding mode control to improve the control accuracy and stability, and to enhance the control process hierarchy, specificity and effectiveness. At the kinematic level, the trajectory tracking error model is established, which is transformed into a quadratic programming problem, and constraints are added to solve the optimal solution of the quadratic programming online with the rolling optimization of the model predictive control, and the AGV pose error is converted into the expected output of the wheel speed. At the dynamic level, sliding mode control is used to obtain the wheel torque output and to realize the wheel’s tracking of the expected speed. The ELM (Extreme Learning Machine) neural network with fast and accurate approximation ability is introduced to carry out online observation of the model uncertainty and unknown interference, and the adaptive interference is offset in combination with sliding mode control to further improve the robustness of the controller. Under the conditions of cosine disturbance and pulse interference, the controller is simulated and verified. Compared with PID control, the MPC+SMC cascade controller has obvious advantages in tracking effect. Moreover, compared with the cascade controller observed by RBF (Radial Basis Function) neural network, the ELM observer is more robust to interference, for instance, the observation effect remains above 95% under various rotational speed conditions, the tracking error of the proposed control method is one order of magnitude smaller than other methods in multiple indicators, with a maximum deviation of only millimeters. Finally, an experimental platform is set up to perform actual trajectory tracking experiment, and the results verify the practicability and feasibility of the proposed controller.