Origin-Destination (OD) prediction which aims to predict the number of passenger’s travel demands from one region to another, is critically important to many real applications including intelligent transportation systems and public safety. The challenges of this problem lie in both the dynamic patterns of the human mobility data and data sparsity in issue in some regions. Thus it is difficult to model the complex spatio-temporal correlations of the human mobility data to predict the OD of their trips. Meanwhile, the crowd flows in different regions of a city and the context features (e.g. holiday, weather and POIs) are potentially useful to alleviate the data sparsity issue and improve the OD prediction, but are largely ignored by existing works. In this paper, we propose a deep spatio-temporal framework which named Auxiliary-tasks Enhanced Spatio-Temporal Network (AEST) to more effectively address the OD prediction problem. AEST trains a model to conduct OD inference via learning crowd flow and external data as auxiliary task. The novel Hierarchical Convolutional LSTM (HC-LSTM) Network is proposed which combines CNN, GCN and LSTM to effectively capture spatiao-temporal correlations. In addition, we design a Contextual Network (ContextNet) which learns representations of contextual information to assist OD prediction. We conduct extensive experiments over bike and taxicab trip datasets in New York. The results show that our method is superior to the state-of-art approaches.