Rapid and accurate detection of crowd abnormal events, such as stampedes and violent attacks in public places, has great research significance and application value. Due to the diversity and uncertainty of abnormal events, almost all existing methods tackle the problem by minimizing the reconstruction errors of training data, which cannot guarantee a larger reconstruction error for all abnormal events. According to the idea that “normal events can be predicted, abnormal events cannot be predicted,” we proposed a future frame prediction-based anomaly detection algorithm. First, the generative adversarial network (GAN) is trained by the normal videos to predict normal future frames. Then, it can determine the existence of abnormal events by identifying the difference between the ground truth and predicted video frame. In the design of the GAN, the attention module is introduced to improve the prediction level of the network. At the same time, the optical flow information is added for motion constraint to improve the constraint ability on the appearance characteristics. In the testing stage, the appearance gap and optical flow gap between the ground truth and the predicted video frame are fused to determine whether the frame is abnormal. The experimental results on the datasets of CUHK Avenue, UCSD, and ShanghaiTech show that the proposed algorithm is superior to that of the current mainstream anomaly detection algorithms.