This paper proposes a self tuning fuzzy inference method by the genetic algorithm in the fuzzy-sliding mode control for a robot. Using this method, the number of inference rules and the shape of membership functions are optimized without an expert in robotics. The fuzzy outputs of the consequent part are updated by the gradient descent method. And, it is guaranteed that he selected solution become the global optimal solution by optimizing the Akaikes information criterion expressing the quality of the inference rules. The trajectory tracking simulation and experiment of the polishing robot show that the optimal fuzzy inference rules are automatically selected by the genetic algorithm and the proposed fuzzy-sliding mode controller provides reliable tracking performance during the polishing process.