We aim for realizing a robotic system that hands over necessary objects to a user as soon as he/she attempts to reach out for it. In this study, we adopt self-moving trays as robots. In order to hand the objects to the user, the system has to predict the user's hand movements and adapt to them. In this paper, we propose a method to predict durations and final positions of reaching movements of the user's hand. We apply the minimum jerk model to the prediction and estimate parameters of the model by using Levenberg-Marquardt method. A description of the experimental results demonstrates the usefulness of the method proposed here.