This paper focuses on the teleoperation of a robot hand on the basis of finger position recognition and grasp type estimation. For the finger position recognition, we propose a new method that fuses machine learning and high-speed image-processing techniques. Furthermore, we propose a grasp type estimation method according to the results of the finger position recognition by using decision tree. We developed a teleoperation system with high speed and high responsiveness according to the results of the finger position recognition and grasp type estimation. By using the proposed method and system, we achieved teleoperation of a high-speed robot hand. In particular, we achieved teleoperated robot hand control beyond the speed of human hand motion.