Alzheimer's disease (AD) is an irreversible neurodegenerative disorder with progressive impairment of memory and cognitive functions. Its early diagnosis is crucial for development of future treatment. Magnetic resonance images (MRI) play important role to help understand the brain anatomical changes related to AD. Conventional methods extract the hand-crafted features such as gray matter volumes and cortical thickness and train a classifier to distinguish AD from other groups. Different from these methods, this paper proposes to construct multiple deep 3D convolutional neural networks (3D-CNNs) to learn the various features from local brain images which are combined to make the final classification for AD diagnosis. First, a number of local image patches are extracted from the whole brain image and a 3D-CNN is built upon each local patch to transform the local image into more compact high-level features. Then, the upper convolution and fully connected layers are fine-tuned to combine the multiple 3D-CNNs for image classification. The proposed method can automatically learn the generic features from imaging data for classification. Our method is evaluated using T1-weighted structural MR brain images on 428 subjects including 199 AD patients and 229 normal controls (NC) from Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Experimental results show that the proposed method achieves an accuracy of 87.15% and an AUC (area under the ROC curve) of 92.26% for AD classification, demonstrating the promising classification performances.