Novel coronavirus disease 2019 (COVID-19) has rapidly spread throughout the world; however, it is difficult for clinicians to make early diagnoses. This study is to evaluate the feasibility of using deep learning (DL) models to identify asymptomatic COVID-19 patients based on chest CT images. In this retrospective study, six DL models (Xception, NASNet, ResNet, EfficientNet, ViT, and Swin), based on convolutional neural networks (CNNs) or transformer architectures, were trained to identify asymptomatic patients with COVID-19 on chest CT images. Data from Yangzhou were randomly split into a training set (n = 2140) and an internal-validation set (n = 360). Data from Suzhou was the external-test set (n = 200). Model performance was assessed by the metrics accuracy, recall, and specificity and was compared with the assessments of two radiologists. A total of 2700 chest CT images were collected in this study. In the validation dataset, the Swin model achieved the highest accuracy of 0.994, followed by the EfficientNet model (0.954). The recall and the precision of the Swin model were 0.989 and 1.000, respectively. In the test dataset, the Swin model was still the best and achieved the highest accuracy (0.980). All the DL models performed remarkably better than the two experts. Last, the time on the test set diagnosis spent by two experts—42 min, 17 s (junior); and 29 min, 43 s (senior)—was significantly higher than those of the DL models (all below 2 min). This study evaluated the feasibility of multiple DL models in distinguishing asymptomatic patients with COVID-19 from healthy subjects on chest CT images. It found that a transformer-based model, the Swin model, performed best.