Objective. Brain 18F-FDG PET images indicate brain lesions’ metabolic status and offer the predictive potential for Alzheimer’s disease (AD). However, the complexity of extracting relevant lesion features and dealing with extraneous information in PET images poses challenges for accurate prediction. Approach. To address these issues, we propose an innovative solution called the efficient adaptive multiscale network (EAMNet) for predicting potential patient populations using positron emission tomography (PET) image slices, enabling effective intervention and treatment. Firstly, we introduce an efficient convolutional strategy to enhance the receptive field of PET images during the feature learning process, avoiding excessive extraction of fine tissue features by deep-level networks while reducing the model’s computational complexity. Secondly, we construct a channel attention module that enables the prediction model to adaptively allocate weights between different channels, compensating for the spatial noise in PET images’ impact on classification. Finally, we use skip connections to merge features from different-scale lesion information. Through visual analysis, the network constructed in this article aligns with the regions of interest of clinical doctors. Main results. Through visualization analysis, our network aligns with regions of interest identified by clinical doctors. Experimental evaluations conducted on the ADNI (Alzheimer’s Disease Neuroimaging Initiative) dataset demonstrate the outstanding classification performance of our proposed method. The accuracy rates for AD versus NC (Normal Controls), AD versus MCI (Mild Cognitive Impairment), MCI versus NC, and AD versus MCI versus NC classifications achieve 97.66%, 96.32%, 95.23%, and 95.68%, respectively. Significance. The proposed method surpasses advanced algorithms in the field, providing a hopeful advancement in accurately predicting and classifying Alzheimer’s Disease using 18F-FDG PET images. The source code has been uploaded to https://github.com/Haoliang-D-AHU/EAMNet/tree/master.