Resting state functional magnetic resonance imaging (rs-fMRI) can explain the connectivity of different regions in the human brain, and thus explain the disease through the different states of brain regions. However, fMRI imaging is complex, and understanding it usually requires a high threshold, while deep learning can enable more non-medical professionals to participate in auxiliary diagnosis research. Therefore, based on rs-fMRI data and deep learning methods, this paper attempts to achieve the classification of early stages Alzheimer’s disease. We used the data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. It contains 313 complete samples from 177 subjects. We used SPM12 to perform necessary preprocessing on the data, and then divided the data into 94 brain regions based on the AAL template. Subsequently, we calculated the graph theory coefficients for each brain region and applied the fisher-score to select important regions. Mixup data augmentation was then applied for generating more items. Finally, a dual-branch CNN-LSTM network was built to classify the obtained correlation coefficients. The model finally achieved good results of accuracy = 0.859 for the four stages prediction of Alzheimer’s Disease (AD), Early Mild Cognitive Impairment (EMCI), Late Mild Cognitive Impairment (LMCI), and Cognitively Normal (CN).