Functional hyper-networks are widely used in brain disease diagnosis and classification studies. However, the existing research on hyper-network construction lacks the ability to interpret the grouping effect or only considers the information of group level information of brain regions, the hyper-network constructed in this way may lose some useful connections or contain some false information. Therefore, considering the group structure problem of brain regions, the sparse group Lasso (Least absolute shrinkage and selection operator) (sgLasso) method was introduced to further improve the construction of hyper-network. Firstly, the hyper-network was constructed by using the sgLasso method. Then, two groups of attribute indicators specific to the hyper-network were introduced for feature extraction and feature selection. The indictors are the clustering coefficient based on single node and the clustering coefficient based on a pair of nodes. Finally, the two groups of features with significant difference obtained after feature selection were subjected to multi-kernel learning for feature fusion and classification. The experimental results show that the proposed method achieves 87.88% classification accuracy by using the multi-feature fusion, which indicates that in order to improve the construction of hyper-network of brain function, the group information should be considered, but the whole group information cannot be forced to be used, and the group structure can be appropriately expanded.