This paper proposes a novel combination of neural network model predictive control with active disturbance rejection for trajectory tracking of a 4 degrees of freedom robot manipulator. The method leverages a neural network for accurate, derivative-free prediction of robot dynamics, enabling the neural network model predictive controller to perform effective trajectory tracking while handling constraints. A terminal cost stabilizing constraint is introduced to the optimization problem to ensure stability, and the optimal control action is computed using the Archimedes optimization algorithm. Crucially, the integrated active disturbance rejection controller, utilizing an extended state observer, provides real-time estimation and compensation of total disturbances, significantly enhancing the system’s robustness against external disturbances and internal uncertainties arising from unmodeled dynamics and parameter uncertainties. The effect of the total disturbances is then dynamically compensated by subtracting their estimation from the control law of the neural network model predictive controller. Experimental validation on the MICO robot manipulator provides concrete evidence that the proposed strategy achieves superior tracking performance and significantly improved disturbance rejection compared to neural network model predictive controller and fractional power rate sliding mode controller. These experimental findings confirm the practical applicability and advanced performance of the proposed controller.