Alzheimer's disease (AD) is an irreversible neurode generative disease of the brain.The disease may causes memory loss, difficulty communicating and disorientation. For the diagnosis of Alzheimer's disease, a series of scales are often needed to evaluate the diagnosis clinically, which not only increases the workload of doctors, but also makes the results of diagnosis highly subjective. Therefore, for Alzheimer's disease, imaging means to find early diagnostic markers has become a top priority. In this paper, we propose a novel 3DMgNet architecture which is a unified framework of multigrid and convolutional neural network to diagnose Alzheimer's disease (AD). The model is trained using an open dataset (ADNI dataset) and then test with a smaller dataset of ours. Finally, the model achieved 92.133% accuracy for AD vs NC classification and significantly reduced the model parameters.