Automatic and accurate classification of Alzheimer’s disease is a challenging and promising task. Fully Convolutional Network (FCN) can classify images at the pixel level. Adding an attention mechanism to the Fully Convolutional Network can effectively improve the classification performance of the model. However, the self-attention mechanism ignores the potential correlation between different samples. Aiming at this problem, we propose a new method for image classification of Alzheimer’s disease based on the external-attention mechanism. The external-attention module is added after the fourth convolutional block of the fully convolutional network model. At the same time, the double normalization method of Softmax and L1 norm is introduced to obtain a better classification performance and richer feature information of the disease probability map. The activation function Softmax can increase the degree of fitting of the neural network to the training set, which transforms linearity into nonlinearity, thereby increasing the flexibility of the neural network. The L1 norm can avoid the attention map being affected by especially large (especially small) eigenvalues. The experiments in this paper use 550 three-dimensional MRI images and use five-fold cross-validation. The experimental results show that the proposed image classification method for Alzheimer’s disease, combining the external-attention mechanism with double normalization, can effectively improve the classification performance of the model. With this method, the accuracy of the MLP-A model is 92.36%, the accuracy of the MLP-B model is 98.55%, and the accuracy of the fusion model MLP-C is 98.73%. The classification performance of the model is higher than similar models without adding any attention mechanism, and it is better than other comparison methods.