In order to solve the contradiction between the positioning accuracy in the traditional star selection algorithm and the complexity for calculating the Geometric Dilution of Precision (GDOP), an improved fast satellite selection algorithm is proposed. By using the elevation angle and azimuth information of the satellite to divide the region, the satellite with signal-to-noise ratio less than a certain threshold is eliminated, and the GDOP calculation method of Newton's identity is used to finally determine the selection of six satellites for positioning. The optimal satellite geometric distribution region for less period calculation can greatly reduce the amount of computation.Theoretical analysis and experimental results show that:Compared with the minimum GDOP algorithm, the proposed algorithm has a significant reduction on computation amount when the positioning accuracy is slightly sacrificed, and the positioning accuracy is higher than that of the Quasi-Optimal algorithm, which proves the effectiveness of the algorithm.