Receiver autonomous integrity monitoring (RAIM) is an effective method for global satellite navigation system (GNSS) integrity monitoring, and the current problem of insufficient availability of RAIM will limit the application of satellite navigation system in the precision approach phase. In view of this situation, the positioning influence caused by satellite minor fault is first analyzed, and then an improved RAIM algorithm based on BP neural network is proposed. The traditional RAIM algorithm is improved by taking advantage of BP neural network being more sensitive to nonlinear relationships, so as to improve the detection performance of satellite minor fault and improve the navigation performance of the navigation system. Finally, the algorithm proposed in this paper is evaluated. The experimental results show that the improved RAIM algorithm based on BP neural network can significantly improve the ability of satellite minor fault detection, so that the satellite navigation system can meet the performance requirements of LPV-200, that is, improve the availability of RAIM in the precision approach phase.