We present BiPOCO, a Bi-directional trajectory predictor with POse COnstraints, for detecting anomalous activities of pedestrians in videos. In contrast to prior work based on feature reconstruction, our work identifies pedestrian anomalous events by forecasting their future trajectories and comparing the predictions with their expectations. We introduce a set of novel compositional pose-based losses with our predictor and leverage prediction errors of each body joint for pedestrian anomaly detection. Experimental results show that our BiPOCO approach can detect pedestrian anomalous activities with a high detection rate (up to 87.0%) and incorporating pose constraints helps distinguish normal and anomalous poses in prediction. This work extends current literature of using prediction-based methods for anomaly detection and can benefit safety-critical applications such as autonomous driving and surveillance. Code is available at https://github.com/akanuasiegbu/BiPOCO.