We develop an end-to-end deep learning-based anomaly detection model for temporal data in transportation networks. The proposed EVT-LSTM model is derived from the popular LSTM (Long Short-Term Memory) network and adopts an objective function that is based on fundamental results from EVT (Extreme Value Theory). We compare the EVT-LSTM model with some established statistical, machine learning, and hybrid deep learning baselines. Experiments on seven diverse real-world data sets demonstrate the superior anomaly detection performance of our proposed model over the other models considered in the comparison study.