Stability control is critical to the exoskeleton robot controller design. Considering the complex structural characteristics of lower limb exoskeleton robots, the major challenge of the controller design is the accuracy and uncertainty of the dynamics model. To fill in this research gap, this study proposes successive approximation-based radial basis function (RBF) neural networks (NNs). The proposed model simplifies the lower limb exoskeleton robot as three degrees-of-freedom (3-DOF) model with the human hip joints for adduction/extension, bending/extension, and internal/external rotation. To minimize the gait tracking errors and stabilize the closed-loop system, a gait trajectory-based control and approximation model was proposed in this study. To verify the proposed method, a validation experiment was conducted for typical lower limb motions. The experiment results demonstrated the effectiveness of the proposed method.