COVID-19 is an infectious pneumonia caused by 2019-nCoV. The number of newly confirmed cases and confirmed deaths continues to remain at a high level. RT–PCR is the gold standard for the COVID-19 diagnosis, but the computed tomography (CT) imaging technique is an important auxiliary diagnostic tool. In this paper, a deep learning network mutex attention network (MA-Net) is proposed for COVID-19 auxiliary diagnosis on CT images. Using positive and negative samples as mutex inputs, the proposed network combines mutex attention block (MAB) and fusion attention block (FAB) for the diagnosis of COVID-19. MAB uses the distance between mutex inputs as a weight to make features more distinguishable for preferable diagnostic results. FAB acts to fuse features to obtain more representative features. Particularly, an adaptive weight multiloss function is proposed for better effect. The accuracy, specificity and sensitivity were reported to be as high as 98.17%, 97.25% and 98.79% on the COVID-19 dataset-A provided by the Affiliated Medical College of Qingdao University, respectively. State-of-the-art results have also been achieved on three other public COVID-19 datasets. The results show that compared with other methods, the proposed network can provide effective auxiliary information for the diagnosis of COVID-19 on CT images.