Angles-Only initial orbit determination (IOD) is the key to space object cataloguing for optical observation systems. For space objects in Low Earth Orbit (LEO), the observed arcs obtained by ground-based optical observation systems are too short and without range information. Therefore, the IOD results of them have large errors and are unusable in further studies. For this reason, this paper studies the non-cooperative common-view observation technology of LEO space objects and relevant initial orbit determination. Based on statistics, a new method of space object positioning by non-cooperative common-view observation technique is proposed. With optical observations from the space object and debris observation network of the Chinese Academy of Sciences, the experiment is conducted to validate the proposed method. The results show that the root mean square (RMS) error of the proposed method is less than 100 m for the satellite Ajisai and that is less than 200 m for the space debris CZ-2C R/B, which means this method is better than the traditional trigonometric parallax method. The positioning results are then used to IOD, and the obtained semi-major axis errors are around 1 km.