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Dialogue state tracking (DST) aims at estimating the current dialogue state given all the preceding conversation. For multi-domain DST, the data sparsity problem is also a major obstacle due to the increased number of state candidates. Existing approaches generally predict the value for each slot independently and do not consider slot relations, which may aggravate the data sparsity problem. In this paper, we propose a Schema-guided multi-domain dialogue State Tracker with graph attention networks (SST) that predicts dialogue states from dialogue utterances and schema graphs which contain slot relations in edges. We also introduce a graph attention matching network to fuse information from utterances and graphs, and a recurrent graph attention network to control state updating. Experiment results show that our approach obtains new state-of-the-art performance on both MultiWOZ 2.0 and MultiWOZ 2.1 benchmarks.