In public places, some behavior that violates public order and endangers public safety is defined as abnormal behavior. Moreover, it is a necessary auxiliary means to maintain public order and safety by detecting abnormal behavior in a large number of surveillance videos. However, due to the small proportion of abnormal behavior in video data, the extreme imbalance of data seriously restricts the effectiveness of detection. So, weakly supervised learning has become the most suitable and effective detection method. However, existing weakly supervised methods rarely take the locality and slightness of abnormal behavior into account and ignore the details of extracted features. Based on this, an attention-directed abnormal behavior detection model is proposed. In the two common prediction and reconstruction abnormal behavior detection methods based on weak supervision, suitable attention mechanisms are introduced, respectively, and two corresponding attention-directed networks are proposed. In addition, aiming at the problem of inaccurate thresholds for abnormal behavior division, the loss function of the model is improved and a new abnormal behavior evaluation method is proposed. Experiments were carried out on three classical datasets (the USCD Ped1, USCD Ped2, and CUHK Avenue dataset) for abnormal behavior detection. The best results for the area under the curve (AUC) indicator reached 82.7%, 94.5%, and 87.3%, respectively, which are better than many existing literature results.