Background: Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder that has become one of the major health concerns for the elderly. Computer-aided AD diagnosis can assist doctors in quickly and accurately determining patients' severity and affected regions. Methods: In this paper, we propose a method called MADNet for computer-aided AD diagnosis using multimodal datasets. The method selects ResNet-10 as the backbone network, with dual-branch parallel extraction of discriminative features for AD classification. It incorporates long-range dependencies modeling using attention scores in the decision-making layer and fuses the features based on their importance across modalities. To validate the effectiveness of our proposed multimodal classification method, we construct a multimodal dataset based on the publicly available ADNI dataset and a collected XWNI dataset, which includes examples of AD, Mild Cognitive Impairment (MCI), and Cognitively Normal (CN). Results: On this dataset, we conduct binary classification experiments of AD vs. CN and MCI vs. CN, and demonstrate that our proposed method outperforms other traditional single-modal deep learning models. Furthermore, this conclusion also confirms the necessity of using multimodal sMRI and DTI data for computer-aided AD diagnosis, as these two modalities complement and convey information to each other. We visualize the feature maps extracted by MADNet using Grad-CAM, generating heatmaps that guide doctors' attention to important regions in patients' sMRI, which play a crucial role in the development of AD, establishing trust between human experts and machine learning models. Conclusion: We propose a simple yet effective multimodal deep convolutional neural network model MADNet that outperforms traditional deep learning methods that use a single-modality dataset for AD diagnosis.