Mobile robots have been widely engaged in many fields. To obtain the precise and consistent localization of mobile robots, the Global Navigation Satellite System (GNSS) is often employed. With the continuous development and modernization of GNSS, more tracked satellites can be used for multi-GNSS positioning calculation, which can improve the positioning performance and enhance accuracy. However, it also increases computational complexity. Therefore, a satellite selection method, which selects a subset from all visible satellites, is necessary. In multi-GNSS positioning, the geometric dilution of precision (GDOP) is an essential metric for satellite selection. However, the traditional traversal method requires a large amount of solution resources. In this paper, we proposed an improved genetic algorithm for satellite selection. By defining the maturity factor (MF) to guide the crossover and mutation operators, the search performance is guaranteed while reducing unnecessary crossover and mutation operations, thus reducing the search time. By adopting the previous epoch optimal individual inheritance strategy, the satellite selection results of subsequent epochs under continuous epochs have been improved. The experimental results verify the effectiveness of the proposed method.