GPS is being increasingly used in critical infrastructures in modern society. Therefore, the reliability of GPS is extremely important. Recently, the vulnerability of GPS to a spoofing attack has been discussed in the literature. A malicious attacker may spoof a GPS receiver, causing it to provide incorrect navigation and timing information, which may lead to serious damage. Therefore, it is extremely important to detect spoofing attacks as quickly as possible. In this paper, we propose a quickest spoofing detection algorithm to combat GPS spoofing attacks. The experimental results demonstrate that the proposed algorithm can effectively detect the spoofing attack quickly after it occurs.