Unsupervised cross-domain NER task aims to solve the issues when data in a new domain are fully-unlabeled. It leverages labeled data from source domain to predict entities in unlabeled target domain. Since training models on large domain corpus is time-consuming, in this paper, we consider an alternative way by introducing syntactic dependency structure. Such information is more accessible and can be shared between sentences from different domains. We propose a novel framework with dependency-aware GNN (DGNN) to learn these common structures from source domain and adapt them to target domain, alleviating the data scarcity issue and bridging the domain gap. Experimental results show that our method outperforms state-of-the-art methods.