Mild cognitive impairment (MCI) is the early stage of Alzheimer's disease, which is associated with abnormal brain proteins, the recognition of MCI being a challenging task. Recent studies have shown that the performance of MCI identification can be improved by combining protein features captured in Positron Emission Computed Tomography(PET). Nevertheless, there are still great challenges in extracting effective features from the vast amount of information. Most brain networks only considered the unilateral features of nodes or edges, ignored the interactions between them. In response to this problem, our study proposed to combine the quadruple Siamese network and GCN with self-attention pooling(QS-SAGCN) for MCI identification. In detail, we constructed the multiple protein features network(MPN) and higher-order MPN(MPHN) by PET images to promote the MCI identification. Furthermore, a pooling operation with self-attention mechanism was incorporated into GCN(SAGCN), which considered the node characteristics and topology in the graph network to facilitate the acquisition of robust biomarkers, simultaneously. Additionally we combined quadruple Siamese network with SAGCN as classification framework to improve the identification accuracy. Our proposed MCI identification method was evaluated on 230 subjects (including 117 MCI subjects, 113 normal control subjects) with both 18F-AV-1451 PET and 18F-AV-45 PET data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. Experimental results showed that 1) QS-SAGCN enhanced the ability of feature identification, laying the foundation for obtaining more effective biomarkers for MCI patients; 2) The MCI identification accuracy (93.5%) was obtained by combining QS-SAGCN and higher-order network, indicating that the framework had advantages in mental disorders recognition. Finally, through comparison, the accuracy of our proposed MCI recognition method was superior to some of the existing state-of-the-art methods. Overall, the MCI identification method in this study was effective and promising to assist in the diagnosis of MCI in future clinical practice.