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Aiming at the influence of the accuracy of the dynamic model on the self-balancing control of the non-coaxial two-wheeled robot under the conditions of large changes in vehicle speed, body roll angle and front wheel rotation angle in the self-balancing control based on the front wheel rotation angle, the design a self-balancing controller based on fuzzy sliding mode control of radial basis function(RBF) neural network is proposed. Using the approximation characteristics of RBF neural network, the nonlinear time-varying uncertain part of the dynamic model is adaptively approximated, thereby improving the accuracy of the dynamic model. And the system chattering generated in sliding mode control is weakened with the help of fuzzy rules. And because the front wheel angle is used for self-balancing control, it is difficult to achieve steering closed-loop control, a trajectory tracking controller based on pure pursuit method is established, and the coupling relationship between the body roll angle and the front wheel angle when the body is balanced is designed to control the steering closed-loop control. The target front wheel turning angle in the system is replaced with the target body roll angle, so that the self-balancing controller and the trajectory tracking controller are combined to realize the closed-loop steering control with trajectory tracking on the premise of ensuring the balanced driving of the body. The experimental results show that with the high accuracy of the dynamic model, the RBF neural network fuzzy sliding mode self-balancing controller has the advantages of good robustness, low overshoot and fast response, and uses the body to balance the rear body roll angle and the front. It is feasible to realize the steering closed-loop control based on the coupling relationship of the wheel rotation angle, and has a good trajectory tracking effect.