The accurate forecasting of urban taxi demands, which is a hot topic in intelligent transportation research, is challenging due to the complicated spatial-temporal dependencies, the dynamic nature, and the uncertainty of traffic. To make full use of the global and local correlations between traffic flows on road sections, this paper presents a deep learning model based on a graph convolutional network, long short-term memory (LSTM), and multitask learning. First, an undirected graph model was formed by considering the spatial pattern distribution of taxi trips on road networks. Then, LSTMs were used to extract the temporal features of traffic flows. Finally, the model was trained using a multitask learning strategy to improve the model’s generalizability. In the experiments, the efficiency and accuracy were verified with real-world taxi trajectory data. The experimental results showed that the model could effectively forecast the short-term taxi demands on the traffic network level and outperform state-of-the-art traffic prediction methods.