Alzheimer’s Disease (AD) is a neurodegenerative disease, typically identified and diagnosed through brain biometric feature. However, certain common brain biometric feature exist among patients in different stages of AD, which result in incorrect edges within the graph structure. To address above issues, this paper proposes a Graph Structure-Feature Learning Network (GSFLN) model. The model simultaneously learns a graph structure that appropriately represents the relationships among patients and selects the significant pathogenic brain biometric feature of patients. Firstly, a Graph Convolutional Clustering (GCC) module is designed to capture the relationships between non-image data of patients. Secondly, a Pathogenic Feature Selection (PFS) module is designed to capture the relationships between image data of patients and select the pathogenic brain biometric feature. Thirdly, an Unsupervised Predictive Clustering (UPC) module is designed to control the above two modules. Our proposed model has surpassed the current state-of-the-art level in diagnostic performance on both the NACC and Tadpole datasets.