Prediction of couriers’ delivery timely rates in advance is essential to the logistics industry, enabling companies to take preemptive measures to ensure the normal operation of delivery services. This becomes even more critical during anomaly conditions like the epidemic outbreak, during which couriers’ delivery timely rate will decline markedly and fl uctuates signifi cantly. Existing studies pay less attention to the logistics scenario. Moreover, many works focusing on prediction tasks in anomaly scenarios fail to explicitly model abnormal events, e.g., treating external factors equally with other features, resulting in great information loss. Further, since some anomalous events occur infrequently, traditional data-driven methods perform poorly in these scenarios. To deal with them, we propose a deep spatial-temporal attention model, named DeepSTA. To be specific, to avoid information loss, we design an anomaly spatio-temporal learning module that employs a recurrent neural network to model incident information. Additionally, we utilize Node2vec to model correlations between road districts, and adopt graph neural networks and long short-term memory to capture the spatial-temporal dependencies of couriers. To tackle the issue of insuffi cient training data in abnormal circumstances, we proposean anomaly pattern attention module that adopts a memory network for couriers’ anomaly feature patterns storage via attention mechanisms. The experiments on real-world logistics datasets during the COVID-19 outbreak in 2022 show the model outperforms the best baselines by 12.11% in MAE and 13.71% in MSE, demonstrating its superior performance over multiple competitive baselines.