Alzheimer's disease(AD) is a kind of progressive neurodegenerative disease. One who is diagnosed as an Alzheimer's disease patient may has many symptoms, such as deterioration of memory and language. Once those symptoms was noticed, they usually can survive 4 to 20 years. So far, Alzheimer's disease has become the sixth leading cause of death, and it has become a worldwide health and social challenge. Traditional methods of diagnosing AD and mild cognitive impairment(MCI), mostly depend on capturing features from variable modalities of brain image data. It is a big challenge to pick out the MCI from normal controller (NC) and AD, especially for those who are lacking experience. In this article, we employ deep convolutional neural network (DCNN) to extract the most useful features of the structural magnetic resonance imaging (MRI). Firstly, the structural MRls are pre-processed in a strict pipeline. Then, instead of parcellating regions of interest, we re-slice each volume, and put the resliced images into a DCNN directly. Finally, four stages of Alzheimer's are identified, and the average accuracy is 94.5% for NC versus LMCI, 96.9% for NC versus AD, 97.2% for LMCI and AD, 97.81 % for EMCI versus AD, 94.8% for LMCI versus EMCI. The results show that the DCNN outperforms existing methods.