Region duplication is one of the most common methods of video forgery. Existing forgery detection algorithms generally suffer from inefficiency and are not effective for the forged regions with mirroring. To address these problems, we present a fast forgery detection algorithm based on Exponential-Fourier moments (EFMs) for detecting region duplication in videos. The algorithm first extracts EFMs features from each block in the current frame, and performs a fast match to find potential matching pairs. Then, a postverification scheme is designed to eliminate falsely matched pairs and locate the altered regions in the current frame. Finally, an adaptive parameter-based fast compression tracking algorithm is used to track the tampered regions in the subsequent frames. The experimental results show that our proposed algorithm has higher detection accuracy and computational efficiency than those of previous algorithms.