Understanding and classifying Chest X-Ray (CXR) and computerised tomography (CT) images are of great significance for COVID-19 diagnosis. The existing research on the classification for COVID-19 cases faces the challenges of data imbalance, insufficient generalisability, the lack of comparative study, etc. To address these problems, this paper proposes a type of modified MobileNet to classify COVID-19 CXR images and a modified ResNet architecture for CT image classification. In particular, a modification method of convolutional neural networks (CNN) is designed to solve the gradient vanishing problem and improve the classification performance through dynamically combining features in different layers of a CNN. The modified MobileNet is applied to the classification of COVID-19, Tuberculosis, viral pneumonia (with the exception of COVID-19), bacterial pneumonia and normal controls using CXR images. Also, the proposed modified ResNet is used for the classification of COVID-19, non-COVID-19 infections and normal controls using CT images. The results show that the proposed methods achieve 99.6% test accuracy on the five-category CXR image dataset and 99.3% test accuracy on the CT image dataset. Six advanced CNN architectures and two specific COVID-19 detection models, i.e., COVID-Net and COVIDNet-CT are used in comparative studies. Two benchmark datasets and a CXR image dataset which combines eight different CXR image sources are employed to evaluate the performance of the above models. The results show that the proposed methods outperform the comparative models in classification accuracy, sensitivity, and precision, which demonstrate their potential in computer-aided diagnosis for healthcare applications.