Early diagnosis is playing an important role in preventing progress of the Alzheimer's disease (AD). This paper proposes to improve the prediction of AD with a deep 3D Convolutional Neural Network (3D-CNN), which can show generic features capturing AD biomarkers extracted from brain images, adapt to different domain datasets, and accurately classify subjects with improved fine-tuning method. The 3D-CNN is built upon a convolutional autoencoder, which is pre-trained to capture anatomical shape variations in structural brain MRI scans for source domain. Fully connected upper layers of the 3D-CNN are then fine-tuned for each task-specific AD classification in target domain. In this paper, deep supervision algorithm is used to improve the performance of already proposed 3D Adaptive CNN. Experiments on the ADNI MRI dataset without skull-stripping preprocessing have shown that the proposed 3D Deeply Supervised Adaptable CNN outperforms several proposed approaches, including 3D-CNN model, other CNN-based methods and conventional classifiers by accuracy and robustness. Abilities of the proposed network to generalize the features learnt and adapt to other domains have been validated on the CADDementia dataset.