Abstract Classical semi-supervised video anomaly detection assumes that only normal data are available in the training set because of the rare and unbounded nature of anomalies. It is obviously, however, these infrequently observed abnormal events can actually help with the detection of identical or similar abnormal events, a line of thinking that motivates us to study open-set supervised anomaly detection with only a few types of abnormal observed events and many normal events available. Under the assumption that normal events can be well predicted, we propose a Margin Learning Embedded Prediction (MLEP) framework. There are three features in MLEP- based open-set supervised video anomaly detection: i) we customize a video prediction framework that favors the prediction of normal events and distorts the prediction of abnormal events; ii) The margin learning framework learns a more compact normal data distribution and enlarges the margin between normal and abnormal events. Since abnormal events are unbounded, our framework consequently helps with the detection of abnormal events, even for anomalies that have never been previously observed. Therefore, our framework is suitable for the openset supervised anomaly detection setting; iii) our framework can readily handle both frame-level and video-level anomaly annotations. Considering that video-level anomaly detection is more easily annotated in practice and that anomaly detection with a few anomalies is a more practical setting, our work thus pushes the application of anomaly detection towards real scenarios. Extensive experiments validate the effectiveness of our framework for anomaly detection