Ride-hailing demand prediction is an important prediction task in traffic prediction. An accurate prediction model can help the platform pre-allocate resources in advance to improve vehicle utilization and reduce the wait-time. This task is challenging due to the complicated spatial-temporal relationships among regions. Most existing methods mainly focus on Euclidean correlations among regions. Though there are some methods that use Graph Convolutional Networks (GCN) to capture the non-Euclidean pair-wise correlations, they only rely on the static topological structure among regions. Besides, they only consider fixed graph structures at different time intervals. In this paper, we propose a novel deep learning method called Spatial-Temporal Dynamic Graph Attention Network (STDGAT) to predict the taxi demand of multiple connected regions in the near future. The method uses Graph Attention Network (GAT), which achieves the adaptive allocation of weights for other regions, to capture the spatial information. Furthermore, we implement a Dynamic Graph Attention mode to capture the different spatial relationships at different time intervals based on the actual commuting relationships. Extensive experiments are conducted on a real-world large scale ride-hailing demand dataset, the results demonstrate the superiority of our method over existing methods.