As the rapid spread of coronavirus disease (COVID-19) worldwide, X-ray chest radiography has also been used to detect COVID-19 infected pneumonia and assess its severity or monitor its prognosis in the hospitals due to its low cost, low radiation dose, and broad accessibility. However, how to more accurately and efficiently detect COVID-19 infected pneumonia and distinguish it from other community-acquired pneumonia remains a challenge. In order to address this challenge, we in this study develop and test a new computer-aided detection and diagnosis (CAD) scheme. It includes pre-processing algorithms to remove diaphragms, normalize X-ray image contrast-to-noise ratio, and generate three input images, which are then linked to a transfer learning based convolutional neural network (VGG16 model) to classify chest X-ray images into three classes of COVID-19 infected pneumonia, other community-acquired pneumonia and normal (non-pneumonia) cases. To this purpose, a publicly available dataset of 8,474 chest X-ray images is used, which includes 415 confirmed COVID-19 infected pneumonia, 5,179 community-acquired pneumonia, and 2,880 non-pneumonia cases. The dataset is divided into two subsets with 90% and 10% of images to train and test the CNN-based CAD scheme. The testing results achieve 93.9% of overall accuracy in classifying three classes and 98.6% accuracy in detecting COVID-19 infected pneumonia cases. The study demonstrates the feasibility of developing a new deep transfer leaning based CAD scheme of chest X-ray images and providing radiologists a potentially useful decision-making supporting tool in detecting and diagnosis of COVID-19 infected pneumonia.