Aiming at the common non-linear relationship between characters in languages， in order to capture richer semantic features， a Named Entity Recognition （NER） method based on Graph Convolutional Network （GCN） and self-attention mechanism was proposed. Firstly， with the help of the effective extraction ability of character features of deep learning methods， the GCN was used to learn the global semantic features between characters， and the Bidirectional Long Short-Term Memory network （BiLSTM） was used to extract the context-dependent features of the characters. Secondly， the above features were fused and their internal importance was calculated by introducing a self-attention mechanism. Finally， the Conditional Random Field （CRF） was used to decode the optimal coding sequence from the fused features， which was used as the result of entity recognition. Experimental results show that compared with the method that only uses BiLSTM or CRF， the proposed method has the recognition precision increased by 2.39% and 15.2% respectively on MicroSoft Research Asia （MSRA） dataset and Biomedical Natural Language Processing/Natural Language Processing in Biomedical Applications （BioNLP/NLPBA） 2004 dataset， indicating that this method has good sequence labeling capability on both Chinese and English datasets， and has strong generalization capability.