With the development of Low-Earth Orbit (LEO) satellite systems, satellite-borne phased array antennas have been applied in satellite systems, providing the conditions for phased array measurement of the Direction of Arrival (DOA) of satellite-borne electromagnetic waves. In the current satellite direction-finding and positioning systems, the single-DOA positioning system is unable to locate aerial targets, and the dual-satellite Time Difference of Arrival (TDOA) and DOA joint positioning system requires synchronized measurement and calculation by two satellites with simultaneous visibility of the target to achieve positioning. To address these issues, a positioning method based on single-satellite dual-DOA is proposed. The principle and algorithm of single-satellite dual-DOA positioning are analyzed. Through simulation, the quantitative impact of different satellite intervals, direction-finding errors, and satellite position errors on the positioning accuracy of satellites is calculated. The Geometric Dilution of Precision (GDOP) of this positioning system is derived, and its feasibility is verified through simulation.