The accuracy of trajectory tracking and stable operation with heavy load are the main challenges of parallel mechanism for wheel-legged robots, especially in complex road conditions. To guarantee the tracking performance in an uncertain environment, the disturbances, including the internal-robot friction and external-robot and environment interaction forces, should be considered in the robot's dynamical system. In this article, a neural fuzzy-based model predictive tracking scheme (NFMPC) for reliable tracking control is proposed to the developed four wheel-legged robot, and the fuzzy neural network approximation is applied to estimate the unknown physical interaction and external dynamics of the robot system. Meanwhile, the advanced parallel mechanism of the four wheel-legged robot (BIT-NAZA) is introduced. Finally, co-simulation and experiment results using the BIT-NAZA robot derived from the proposed hybrid control strategy indicate that the methodology can achieve satisfactory tracking performance in terms of accuracy and stability. This research can provide theoretical and engineering guidance for lateral stability of intelligent robots under unknown disturbances and uncertain nonlinearities, and facilitate the control performance of the wheel-legged robot in a practical system.