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Recently, studies have applied advanced machine learning methods, e.g., convolutional neural network (CNN) and transformer architecture, to extract features from functional connectivity networks (FCNs) for brain disease analysis and classification. However, CNN based methods usually extract local features from FCN, ignoring global representation of FCN. The methods based on transformer extract global features of FCN but are challenging to capture local information of the brain network. To address this problem, in this paper we propose Con-Trans, a novel learning framework that integrates both convolutional operation and transformer for brain disease classification, with functional magnetic resonance imaging (fMRI) data. Experimental results on 174 subjects with resting-state fMRI (rs-fMRI) data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) demonstrate the effectiveness of the proposed Con-Trans method.