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 assume the motion trajectory of a fish swimming in a pool be approximated by a circle with time varying radius and center position. We try to improve prediction accuracy of a fish motion by using N.N. whose inputs are radii and angular velocities in past three control-times and outputs are radius and angular velocity in the following control period. Using radius and angular velocity obtained by circular approximation, we confirmed that the proposed N.N. prediction system can maintain good prediction performances under the proposed on-line learning process.