In recent years, development of mobile service robots has been actively conducted. It is necessary for such a robot to recognize persons reliably. This paper describes a person detection using 3D LIDAR for person tracking with a small robot. Since our LIDAR has a vertical viewing angle of 30 degrees and is put at a low viewpoint, the whole body of a person is not observable if the distance to the person is less than 1.5 m. By adding data of partially observed persons for training, we improved the person detection rate. We evaluated the precision and the recall for the discriminator.