It has been shown that named entity recognition (NER) could benefit from incorporating the long-distance structured information captured by dependency trees. However, dependency trees built by tools usually have a certain percentage of errors. Under such circumstances, how to better use relevant structured information while ignoring irrelevant or wrong structured information from the dependency trees to improve NER performance is still a challenging research problem. In this paper, we propose the Attention and Edge-Label guided Graph Convolution Network (AELGCN) model. Then, we integrate it into BiLSTM-CRF to form BiLSTM-AELGCN-CRF model. We design an edge-aware node joint update module and introduce a node-aware edge update module to explore hidden in structured information entirely and solve the wrong dependency label information to some extent. After two modules, we apply attention-guided GCN, which automatically learns how to attend to the relevant structured information selectively. We conduct extensive experiments on several standard datasets across four languages and achieve better results than previous approaches. Through experimental analysis, it is found that our proposed model can better exploit the structured information on the dependency tree to improve the recognition of long entities.