Alzheimer's disease (AD) is the leading cause of dementia in the elderly and the number of sufferers increases year by year. Early detection of AD is highly beneficial to provide timely treatment and possible medication, which is still an open challenge. To meet challenges of the early diagnosis of AD and its early stage (e.g., progressive MCI (pMCI) and stable MCI (sMCI)) in clinical practice, we present a novel deep learning framework in this paper. The proposed framework exploits the merits of 3D convolutional neural network (CNN) and stacked bidirectional recurrent neural network (SBi-RNN). Specifically, we devise simple 3D-CNN architecture to obtain the deep feature representation from magnetic resonance imaging (MRI) and positron emission tomography (PET) images, respectively. We further apply SBi-RNN on the local deep cascaded and flattened descriptors for performance boosting. Extensive experiments are performed on the ADNI dataset to investigate the effectiveness of the proposed method. Our method achieves an average accuracy of 94.29% for AD vs. normal classification (NC), 84.66% of pMCI vs. NC and 64.47% sMCI vs. NC, which outperforms the related algorithms. Also, our method is simpler and more compact compared with the existing methods with complex preprocessing and feature engineering processes.