Long-term traffic prediction is highly challenging due to thecomplexity of traffic systems and the constantly changing na-ture of many impacting factors. In this paper, we focus on thespatio-temporal factors, and propose a graph multi-attentionnetwork (GMAN) to predict traffic conditions for time stepsahead at different locations on a road network graph. GMAN adapts an encoder-decoder architecture, where both the en-coder and the decoder consist of multiple spatio-temporal attention blocks to model the impact of the spatio-temporal factors on traffic conditions. The encoder encodes the inputtraffic features and the decoder predicts the output sequence. Between the encoder and the decoder, a transform attention layer is applied to convert the encoded traffic features to generate the sequence representations of future time steps as the input of the decoder. The transform attention mechanism models the direct relationships between historical and futuretime steps that helps to alleviate the error propagation problem among prediction time steps. Experimental results on two real-world traffic prediction tasks (i.e., traffic volume prediction and traffic speed prediction) demonstrate the superiority of GMAN. In particular, in the 1 hour ahead prediction, GMAN outperforms state-of-the-art methods by up to 4% im-provement in MAE measure.