Alzheimer′s disease (AD) is a neurodegenerative disease that is a significant contributor to dementia. Accurate diagnosis of Alzheimer′s disease (AD) is of great significance. The integration of multimodal data from Fluorodeoxyglucose positron emission tomography (FDG-PET) and structural magnetic resonance imaging (sMRI) of the brain provides a comprehensive information of lesions from multiple perspectives and enhancing diagnostic accuracy. However, the image data is highly redundant, and the features of the various modes are also significantly disparate. Traditional convolutional neural networks and simple feature concatenation methods are unable to effectively utilize the complementary information of multi-modal data, consequently, this limits the diagnostic performance of AD. To solve this problem, we propose a multimodal image AD classification network combining sMRI and FDG-PET. The network incorporates coordinate attention mechanisms and spatial-channel reconstruction convolution to capture specific regions in images and limit redundant information. A parallel interaction network is also designed, which not only enhances each modality′s own features, but also adaptively adjusts itself according to the features of other modalities, thus realizing effective interaction between modalities. The classification performance of the proposed network is evaluated on the ADNI dataset, and the accuracy, sensitivity, and specificity reach 93.66%、91.67% and 95.41%, respectively, the experimental results show that the proposed network in this paper has a superior performance compared to the existing AD classification networks.