Abstract: The first step is to design a low earth orbit satellite (LEO) for navigation augmentation using low earth orbit satellites. When designing the constellation configuration, the stability and comprehensive cost of the constellation are two important factors to be considered. This paper presents an optimal design method for low earth orbit navigation constellation considering constellation stability and comprehensive cost. First, the Iridium constellation is optimized by genetic algorithm. Compared with Iridium constellation, the mean number of visible satellites increases from 2.3 to 2.9, the standard deviation of visible satellites decreases from 2.3 to 0.7, and the comprehensive cost factor decreases from 5.3 to 4.5, which proves the effectiveness of this method. Then, taking Walker constellation as the basic configuration, the low earth orbit hybrid constellation is optimized by genetic algorithm, considering the navigation performance and comprehensive cost on the basis of ensuring the stability of the hybrid constellation. The optimized low earth orbit hybrid constellation is combined with the BDS constellation. Compared with the BDS, the mean number of visible satellites increases from 6.9 to 9.3, and the standard deviation of visible satellites decreases from 1.1 to 0.4.