Predicting the passenger flow of metro networks is of great importance for traffic management and public safety. However, such predictions are very challenging, as passenger flow is affected by complex spatial dependencies (nearby and distant) and temporal dependencies (recent and periodic). In this paper, we propose a novel deep-learning-based approach, named STGCNNmetro (spatiotemporal graph convolutional neural networks for metro), to collectively predict two types of passenger flow volumes-inflow and outflow-in each metro station of a city. Specifically, instead of representing metro stations by grids and employing conventional convolutional neural networks (CNNs) to capture spatiotemporal dependencies, STGCNNmetro transforms the city metro network to a graph and makes predictions using graph convolutional neural networks (GCNNs). First, we apply stereogram graph convolution operations to seamlessly capture the irregular spatiotemporal dependencies along the metro network. Second, a deep structure composed of GCNNs is constructed to capture the distant spatiotemporal dependencies at the citywide level. Finally, we integrate three temporal patterns (recent, daily, and weekly) and fuse the spatiotemporal dependencies captured from these patterns to form the final prediction values. The STGCNNmetro model is an end-to-end framework which can accept raw passenger flow-volume data, automatically capture the effective features of the citywide metro network, and output predictions. We test this model by predicting the short-term passenger flow volume in the citywide metro network of Shanghai, China. Experiments show that the STGCNNmetro model outperforms seven well-known baseline models (LSVR, PCA-kNN, NMF-kNN, Bayesian, MLR, M-CNN, and LSTM). We additionally explore the sensitivity of the model to its parameters and discuss the distribution of prediction errors.