Anti-spoofing is becoming a crucial technique for applications with high navigation accuracy and reliability requirements. Anti-spoofing technique based on Receiver Autonomous Integrity Monitoring (RAIM) is a good choice for most Global Navigation Satellite System (GNSS) receivers because it does not require any change to the hardware of the receiver. However, the conventional RAIM method can only detect and mitigate a single spoofing signal. Some improved RAIM methods can deal with more spoofing signals, but the computational complexity increases dramatically when the number of satellites in view increase or need additional information. This paper proposes a new RAIM method, called the SRV-RAIM method, which has a very low computation complexity regardless of the number of satellites in view and can deal with any number of spoofing signals. The key to the new method is the spatial distribution characteristic of the Satellites’ Residual Vectors (SRV). In replay or generative spoofing scenarios, the pseudorange measurements of spoofing signals are consistent, the residual vectors of real satellites and those of spoofing satellites have good separation characteristics in spatial distribution. Based on this characteristic, the SRV-RAIM method is proposed, and the simulation results show that the method can separate the real signals and the spoofing signals with an average probability of 86.55% in the case of 12 visible satellites, regardless of the number of spoofing signals. Compared to the conventional traversal-RAIM method, the performance is only reduced by 3.59%, but the computational cost is reduced by 98.3%, so most of the GNSS receivers can run the SRV-RAIM algorithm in time.