To solve the problem that wheeled robot in the path tracking is prone to slip or roll over at a sharp curve, structure of the wheeled robot and its path tracking features are analyzed, and a new Fuzzy-Neural Network (FNN) based path tracking method of two-stage (route and speed) control is proposed. In the first stage, a FNN controller determines the robot’s turning radius by processing robot’s pose information. In the second stage, the secondary controller adjusts angular and linear velocities by taking advantage of the turning radius and condition of the path ahead. The experiments show that the controlled robot can track the planned path accurately and robustly when it runs at high speed; the process of path tracking is stable and no slipping and rolling occur.