Abstract: The deployment of low earth orbit (LEO) navigation satellites is an important supplement to the existing satellite navigation systems and also an effective approach to navigation augmentation. The design of LEO satellite constellation is studied in this paper, in order to optimize its performance in regional navigation augmentation. Different from the near-circular-orbit-based scheme adopted by most LEO constellations for global navigation augmentation, an elliptical-orbit-based constellation scheme is employed in our design. Owing to the slow-motion speed, the large coverage area, and the long residence time of satellites in the apogee of elliptical orbit, the elliptical-orbit-based scheme is specifically suitable for regional navigation augmentation. In addition, under the framework of Flower constellation, the orbit parameter of each satellite is optimized to ensure that the trajectory of its sub-satellite point repeatedly passes through the center of the region, thus extending the zenith crossing time of the satellite. By the aforementioned constellation design, the key navigation performance metrics, such as zenith crossing time, coverage multiplicity, and geometric dilution of precision, are effectively improved. In the simulations with BeiDou-3 system (BDS-3) being the navigation system to be augmented, it is validated that with the same number of LEO satellites, the proposed design achieves better navigation augmentation performance.