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. Graph convolutional networks show the powerful function of modeling based on graph data dependency, which have become a research hotspot in the field of action recognition. This paper mainly summarizes action recognition methods based on graph convolutional networks. There are two main methods of graph convolutional networks: the spectral-based method and the spacial-based method. Firstly, for the two methods, this paper analyzes advantages and disadvantages from different aspects, summarizes their application and development in the field of action recognition. Then, according to the differences of the design of graph network models and algorithms in action recognition, key aspects of network construction are summarized, and the influence of different algorithms on model performance is compared. Finally, according to the problems existing in the action recognition based on graph convolutional networks, future development of graph convolutional networks is prospected.