Detecting COVID-19 from medical images is a challenging task that has excited scientists around the world. COVID-19 started in China in 2019, and it is still spreading even now. Chest X-ray and Computed Tomography (CT) scan are the most important imaging techniques for diagnosing COVID-19. All researchers are looking for effective solutions and fast treatment methods for this epidemic. To reduce the need for medical experts, fast and accurate automated detection techniques are introduced. Deep learning convolution neural network (DL-CNN) technologies are showing remarkable results for detecting cases of COVID-19. In this paper, deep feature concatenation (DFC) mechanism is utilized in two different ways. In the first one, DFC links deep features extracted from X-ray and CT scan using a simple proposed CNN. The other way depends on DFC to combine features extracted from either X-ray or CT scan using the proposed CNN architecture and two modern pre-trained CNNs: ResNet and GoogleNet. The DFC mechanism is applied to form a definitive classification descriptor. The proposed CNN architecture consists of three deep layers to overcome the problem of large time consumption. For each image type, the proposed CNN performance is studied using different optimization algorithms and different values for the maximum number of epochs, the learning rate (LR), and mini-batch (M-B) size. Experiments have demonstrated the superiority of the proposed approach compared to other modern and state-of-the-art methodologies in terms of accuracy, precision, recall and f_score.