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This paper presents a method to predict a fish motion by neural network (N.N.) with on-line learning when a robot is pursuing fish-catching by a net at hand through hand-eye robot visual servoing. We have learned by previous experiments that fish is much smarter than a robot controlled by visual servoing whose escaping strategy is to make a steady state distance error between the net at robot's hand and the fish. To overcome the fish's escaping strategy we propose prediction servoing utilizing estimated future fish position by on-line adjusting N.N. The effectiveness have been proven through visual servoing and fish catching experiments.