A Gantry-Tau-3R mechanism is a family of parallel-serial manipulator with combination of the Gantry-Tau manipulator and the wrist mechanism with ability of generating 6-degree-of-freedom (6-DoF) motion. Recently, the PID controller and fuzzy incremental controller (FIC) are introduced for the manipulator to reduce the tracking error of the end-effector. The PID controller cannot decrease the tracking error because of the extreme nonlinear structure of the Gantry-Tau-3R. Also, the FIC controller has some drawbacks such as slow response and absence of systematic way to develop the controller. In this work, a new neural network-based PID controller is designed and developed to enhance the system performance and decrease the tracking error of the mechanism. The validation of the model is conducted using Simulink, and the outcomes prove the efficiency of the proposed controller in terms of accuracy by minimizing the tracking error.