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This paper presents a non-delayed visual tracking method of a hand-eye robot for a moving target object. The hand-eye robot is constructed from a three degrees of freedom planar manipulator and a single charged-coupled device (CCD) camera that is mounted on the end-effector. The control objective is to keep the target object around the center of the image plane. In many conventional image-based visual servo methods, it is always assumed that the target object is static. Consequently, the visual tracking delay arises when the target object is moving. Although we have already proposed a non-delayed visual tracking method for a moving target object, this method is developed only for a stereo vision robot with two CCD cameras. Therefore, this paper presents such a visual tracking method for the hand-eye robot. The effectiveness of our proposed method is shown by an experiment.