Deep learning has shown great potential to adaptively learn hidden patterns from high dimensional neuroimaging data, so as to extract subtle group differences. Motivated by the convolutional neural networks and prototype learning, we developed a brain-network-based convolutional prototype learning model (BNCPL), which can learn representations that simultaneously maximize inter-class separation while minimize within-class distance. When applying BNCPL to distinguish 208 depressive disorders from 210 healthy controls using resting-state functional connectivity (FC), we achieved an accuracy of 71.0% in multi-site pooling classification (3 sites), with 2.4-7.2% accuracy increase compared to 3 traditional classifiers and 2 alternative deep neural networks. Saliency map was also used to examine the most discriminative FCs learned by the model; the prefrontal-subcortical circuits were identified, which were also correlated with disease severity and cognitive ability. In summary, by integrating convolutional prototype learning and saliency map, we improved both the model interpretability and classification performance, and found that the dysregulation of the functional prefrontal-subcortical circuit may play a pivotal role in discriminating depressive disorders from healthy controls.