Action recognition technology has great application prospects and potential economic value, and is widely used in video surveillance, video retrieval, human-computer interaction, public security and other fields. Although Convolutional Neural Network is widely used, it has limitations in dealing with data of non-Euclidean space. Graph Convolution Network shows the powerful function of modeling based on graph data dependency. It has become a research hotspot in the field of action recognition. This paper mainly summarizes the action recognition method based on Graph Convolution Network. There are two main methods of Graph Convolution Network: spectral-based method and spacial-based method. For the two methods, this paper analyzes the advantages and disadvantages from different aspects, and summarizes their application and development in the field of action recognition. Finally, according to the problems existing in the action recognition based on Graph Convolution Network, the future development of Graph Convolution Network is prospected.