This paper proposes a neural approximation based model predictive control approach for tracking control of a nonholonomic wheel-legged robot in complex environments, which features mechanical model uncertainty and unknown disturbances. In order to guarantee the tracking performance of wheel-legged robots in an uncertain environment, effective approaches for reliable tracking control should be investigated with the consideration of the disturbances, including internal-robot friction and external physical interactions in the robot’s dynamical system. In this paper, a radial basis function neural network (RBFNN) approximation based model predictive controller (NMPC) is designed and employed to improve the tracking performance for nonholonomic wheel-legged robots. Some demonstrations using a BIT-NAZA robot are performed to illustrate the performance of the proposed hybrid control strategy. The results indicate that the proposed methodology can achieve promising tracking performance in terms of accuracy and stability.