We aim to realize a robotic system that hands over a necessary object to a user as soon as he/she attempts to reach out for it. In order to realize such system, the following is required: 1) detection of the reaching movement, 2) prediction of the target object among multiple objects, and 3) handing over the object to a user. In this paper, the first two of them are described and discussed. We apply the smoothness and the speed of the hand movement to distinguish whether the movement is for reaching or not. And in order to predict the target object, we define the certainty according to the relative movement of the hand to each object. To evaluate the performance of the proposed method, we compare the method with the minimum jerk model based approach. A description of the experimental results demonstrates the usefulness of the method proposed here.