Navigation with low Earth orbit (LEO) satellites becomes a popular topic in recent years. In contrast to traditional satellite positioning systems, the power consumption and latency experienced in LEO satellite positioning are much smaller. However, positioning with LEO satellites would not guarantee higher positioning accuracy compared to Global Positioning System (GPS). To this end, we proposed a cooperative positioning method to reduce the positioning error by correcting the position coordinates obtained from LEO satellites. In our method, the relative angles between devices would be estimated by beamforming. We leverage the angles and position information of neighboring devices to correct the position of the target, which is a kind of angle-based method. The simulation results showed that the positioning error can be improved by 36.8 % while the standard deviation of measurement noise is 5 m and the horizontal dilution of precision (HDOP) is 1.57. Moreover, our method has very low complexity, which is suitable for practical use, such as vehicular localization in vehicle-to-everything (V2X).