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BDS receiver autonomous integrity monitoring plays an important role in avionic navigation system. In this paper, RAIM algorithm based on least squares approach is discussed. Least squares approach is used to detect and identify the fault satellite by the pseudo-range residual construction test statistics. The availability analysis of fault detection based on least squares approach of BDS single system is researched. The results show that the RAIM algorithm based on least squares approach can successfully detect and identify the fault satellite. After using the RAIM algorithm to eliminate fault satellite, it can be clearly seen that the positioning accuracy returns to a fault-free state. Moreover, the RAIM algorithm based on least squares is extremely important for the study of BDS satellite navigation and aviation user life safety.