Purpose: This study aimed to develop and validate computer-aided diagnosis (CXDx) system for classification between COVID-19 pneumonia, non-COVID-19 pneumonia, and the healthy on chest X-ray (CXR) images. Materials and Methods: From two public datasets, 1248 CXR images were obtained, which included 215, 533, and 500 CXR images of COVID-19 pneumonia patients, non-COVID-19 pneumonia patients, and the healthy samples. The proposed CADx system utilized VGG16 as a pre-trained model and combination of conventional method and mixup as data augmentation methods. Other types of pre-trained models were compared with the VGG16-based model. Single type or no data augmentation methods were also evaluated. Splitting of training/validation/test sets was used when building and evaluating the CADx system. Three-category accuracy was evaluated for test set with 125 CXR images. Results: The three-category accuracy of the CAD system was 83.6% between COVID-19 pneumonia, non-COVID-19 pneumonia, and the healthy. Sensitivity for COVID-19 pneumonia was more than 90%. The combination of conventional method and mixup was more useful than single type or no data augmentation method. Conclusion: This study was able to create an accurate CADx system for the 3-category classification. Source code of our CADx system is available as open source for COVID-19 research.