Graph representation learning has become a research hotspot in the field of graph deep learning. Most graph neural networks suffer from oversmoothing, and these methods focus on graph node features and pay little attention to the structural features of graphs. In order to improve the representation of graph structural features, this paper proposes a graph classification method based on graph kernel homomorphic network, namely KerGIN. The method first encodes the node features of the graph through Graph Isomorphism Network（GIN）, and then uses the graph kernel method to encode the graph structure. The Nyström method is further used to reduce the dimension of the graph kernel matrix. The graph kernel matrix is aligned with the graph feature matrix with MLP, and the feature encoding and structure encoding of the graph are adaptively weighted and fused through the attention mechanism to obtain the final feature representation of the graph, which enhances the ability to express the structural feature information of the graph. Finally, the model is experimentally evaluated on seven publicly available graph classification datasets: compared with the existing graph representation models, the KerGIN model is able to improve the graph classification accuracy substantially, and it can enhance the ability of GIN to represent the graph structural feature information.