Alzheimer’s disease (AD) is one of the most common diseases causing cognitive impairment in middle-aged and elderly people, and the high cost of the disease poses a challenge for health systems to cope with the expected increasing number of cases in the future. With the advance of aging of the society, China has the largest number of Alzheimer’s disease patients in the world. Therefore, how to diagnose Alzheimer’s disease early and accurately and intervene positively is an urgent problem. In this paper, the improved MultiRes + UNet network is used to effectively segment the brain tissue in the preprocessing. This method expands the convolutional field by null convolution to integrate the global information, mitigates the differences between encoder–decoder features by using MultiRes block and Res path structure, greatly reducing the memory requirement, and improving its accuracy, applicability, and robustness. The non-local means the attention model is introduced to make the mapped organization categories free from noise interference. In the classification problem, this paper adopts the improved VoxCNN network model for binary classification of AD, EMCI, LMCI, and NC. Experiments showed that the model classification performance and the accuracy rate improved significantly with the combined effect of the improved MultiRes + UNet network and VoxCNN network, the binary classification accuracy was 98.35% for AD vs. NC, 89.46% for AD vs. LMCI, 83.95% for LMCI vs. EMCI, and 88.27% for EMCI vs. NC.