With the wide application of deep learning technology in disease diagnosis, especially the outstanding performance of convolutional neural network (CNN) in computer vision and image processing, more and more studies have proposed to use this algorithm to achieve the classification of Alzheimer’s disease (AD), mild cognitive impairment (MCI) and normal cognition (CN). This article systematically reviews the application progress of several classic convolutional neural network models in brain image analysis and diagnosis at different stages of Alzheimer’s disease, and discusses the existing problems and gives the possible development directions in order to provide some references.