Abstract: In recent years, the application of deep learning related to graph structure data has attracted more and more attention. The emergence of graph neural network has made major breakthroughs in the above tasks, such as social networking, natural language processing, computer vision, even life sciences and other fields. The graph neural network can treat the actual problem as the connection between nodes in the graph and the message propagation problem, and the dependence between nodes can be modeled, so that the graph structure data can be handled well. In view of this, the graph neural network model and its application are systematically reviewed. Firstly, the graph convolutional neural network is explained from three aspects: spectral domain, spatial domain and pooling. Then, the graph neural network model based on the attention mechanism and autoencoder is described, and some graph neural network implemented by other methods are supplemented. Secondly, it summarizes the discussion and analysis on whether the graph neural network can be bigger and deeper. Furthermore, four frameworks of graph neural network are summarized. It also explains in detail the application of graph neural network in natural language processing and computer vision, etc. Finally, the future research of graph neural network is prospected and summarized. Compared with existing review articles on graph neural network, it elaborates the knowledge of spectral theory in detail, and comprehensively summarizes the development history of graph convolutional neural network based on the spectral domain. At the same time, a new classification standard, an improved model for the low efficiency of the spatial domain graph convolutional neural network, is given. And for the first time, it summarizes the discussion and analysis of graph neural network expression ability, theoretical guarantee, etc., and adds a new framework model. In the application part, the latest application of graph neural network is explained.