During the classification of Alzheimer’s disease, the hypergraph neural network (HGNN) can extract features from the hypergraph relationship between subjects, which has a good advantage in representing and learning the structure of complex graphs. However, most models directly or indirectly decompose the higher-order complex relationship between subjects represented by hypergraphs into the simple binary relationship for feature learning, without effectively using the higher-order information of hyperedges. Therefore, an Alzheimer’s disease classification model based on the line-hypergraph neural network (L-HGNN) is proposed. The model uses sparse linear regression to represent the multiple correlations between subjects. With the help of the transformation of hypergraphs and line graphs, the higher-order neighborhood information transmission of nodes and the learning of overall structural features of hyperedges are realized in convolutional network models. Meanwhile, a more differentiated node embedding is generated by the attention mechanism, which is then used in the auxiliary diagnosis of Alzheimer’s disease. Compared with the results of two commonly used methods on the ADNI dataset, the experimental results show that the proposed method can effectively improve the classification accuracy and has important application value in the early diagnosis of Alzheimer’s disease.