To develop a deep-learning model that integrates radiomics analysis for enhanced performance of COVID-19 and Non-COVID-19 pneumonia detection using chest X-ray image, two deep-learning models were trained based on a pre-trained VGG-16 architecture: in the 1st model, X-ray image was the sole input; in the 2nd model, X-ray image and 2 radiomic feature maps (RFM) selected by the saliency map analysis of the 1st model were stacked as the input. Both models were developed using 812 chest X-ray images with 262/288/262 COVID-19/Non-COVID-19 pneumonia/healthy cases, and 649/163 cases were assigned as training-validation/independent test sets. In 1st model using X-ray as the sole input, the 1) sensitivity, 2) specificity, 3) accuracy, and 4) ROC Area-Under-the-Curve of COVID-19 vs Non-COVID-19 pneumonia detection were 1) 0.90$pm$0.07 vs 0.78$pm$0.09, 2) 0.94$pm$0.04 vs 0.94$pm$0.04, 3) 0.93$pm$0.03 vs 0.89$pm$0.03, and 4) 0.96$pm$0.02 vs 0.92$pm$0.04. In the 2nd model, two RFMs, Entropy and Short-Run-Emphasize, were selected with their highest cross-correlations with the saliency maps of the 1st model. The corresponding results demonstrated significant improvements (p<0.05) of COVID-19 vs Non-COVID-19 pneumonia detection: 1) 0.95$pm$0.04 vs 0.85$pm$0.04, 2) 0.97$pm$0.02 vs 0.96$pm$0.02, 3) 0.97$pm$0.02 vs 0.93$pm$0.02, and 4) 0.99$pm$0.01 vs 0.97$pm$0.02. The reduced variations suggested a superior robustness of 2nd model design.