Passenger-flow anomaly detection and prediction are essential tasks for intelligent operation of the metro system. Accurate passenger-flow representation is the foundation of them. However, spatiotemporal dependencies, complex dynamic changes, and anomalies of passenger-flow data bring great challenges to data representation. Taking advantage of the time-varying characteristics of data, we propose a novel passenger-flow representation model based on low-rank dynamic mode decomposition (DMD), which also integrates the global low-rank nature and sparsity to explore the spatiotemporal consistency of data and depict abrupt data, respectively. The model can detect anomalies and predict short-term passenger flow conveniently and flexibly. For anomaly detection, we further introduce a strong temporal Toeplitz regularization to characterize the temporal periodic change of data, so as to more accurately detect anomalies. We conduct experiments with smart card transaction data from the Beijing metro system to assess the performance of the model in two use cases. In terms of anomaly detection, the experimental results demonstrate that our method can detect anomalies efficiently, especially for time sequence anomalies. As for short-term prediction, our model is superior to other methods in most cases.