Abstract: Smooth pursuit is one of the five main eye movements in humans, consisting of tracking a steadily moving visual target. Smooth pursuit is a good example of a sensory-motor task that is deeply based on prediction: tracking a visual target is not possible by correcting the error between the eye and the target position or velocity with a feedback loop, but it is only possible by predicting the trajectory of the target. This paper presents a model of smooth pursuit based on prediction and learning. It starts from amodel of the neuro-physiological system proposed by Shibata and Schaal (Shibata et al., Neural Networks, vol. 18, pp. 213-224, 2005). The learning component added here decreases the prediction time in the case of target dynamics already experienced by the system. In the implementation described here, the convergence time is, after the learning phase, 0.8 s.