For effective treatment of Alzheimer’s disease (AD), it is important to identify subjects who are most likely to exhibit rapid cognitive decline. We aimed to develop an automatic image interpretation system based on a deep convolutional neural network (CNN) which can accurately predict future cognitive decline in mild cognitive impairment (MCI) patients using flurodeoxyglucose and florbetapir positron emission tomography (PET). PET images of 139 patients with AD, 171 patients with MCI and 182 normal subjects obtained from Alzheimer’s Disease Neuroimaging Initiative database were used. Deep CNN was trained using 3-dimensional PET volumes of AD and normal controls as inputs. Manually defined image feature extraction such as quantification using predefined region-of-interests was unnecessary for our approach. Furthermore, it used minimally processed images without spatial normalization which has been commonly used in conventional quantitative analyses. Cognitive outcome of MCI subjects was predicted using this network. The prediction accuracy of the conversion of mild cognitive impairment to AD was compared with the conventional feature-based quantification approach. Accuracy of prediction (84.2%) for conversion to AD in MCI patients outperformed conventional feature-based quantification approaches. ROC analyses revealed that performance of CNN-based approach was significantly higher than that of the conventional quantification methods (p < 0.05). Output scores of the network were strongly correlated with the longitudinal change in cognitive measurements (p < 0.05). These results show the feasibility of deep learning as a practical tool for developing predictive neuroimaging biomarker.