Traffic speed prediction, as one of the most important topics in Intelligent Transport Systems (ITS), has been investigated thoroughly in the literature. Nonetheless, traditional methods show their limitation in coping with complexity and high nonlinearity of traffic data as well as learning spatial-temporal dependencies. Particularly, they often neglect the dynamics happening to traffic network. Attention-based models witnessed extensive developments in recent years and have shown its efficacy in a host of fields, which inspires us to leverage graph-attention-based method to handling traffic network speed prediction. In this paper, we propose a novel deep learning framework, Spatial-Temporal Graph Attention Networks (ST-GAT). A graph attention mechanism is adopted to extract the spatial dependencies among road segments. Additionally, we introduce a LSTM network to extract temporal domain features. Compared with previous related research, the proposed approach is able to capture dynamic spatial dependencies of traffic networks. A series of comprehensive case studies on a real-world dataset demonstrate that ST-GAT supersedes existing state-of-the-art results of traffic speed prediction. Furthermore, outstanding robustness against noise and on reduced graphs of the proposed model has been demonstrated through the tests.