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The COVID-19 (Coronavirus disease 2019) pandemic has become a major global threat to human health and well-being. Thus, the development of computer-aided detection (CAD) systems that are capable of accurately distinguishing COVID-19 from other diseases using chest computed tomography (CT) and X-ray data is of immediate priority. Such automatic systems are usually based on traditional machine learning or deep learning methods. Differently from most of the existing studies, which used either CT scan or X-ray images in COVID-19-case classification, we present a new, simple but efficient deep learning feature fusion model, called <math><mrow><mi>U</mi> <mi>n</mi> <mi>c</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> <mi>t</mi> <mi>y</mi> <mi>F</mi> <mi>u</mi> <mi>s</mi> <mi>e</mi> <mi>N</mi> <mi>e</mi> <mi>t</mi></mrow> </math> , which is able to classify accurately large datasets of both of these types of images. We argue that the uncertainty of the model's predictions should be taken into account in the learning process, even though most of the existing studies have overlooked it. We quantify the prediction uncertainty in our feature fusion model using effective Ensemble Monte Carlo Dropout (EMCD) technique. A comprehensive simulation study has been conducted to compare the results of our new model to the existing approaches, evaluating the performance of competing models in terms of Precision, Recall, F-Measure, Accuracy and ROC curves. The obtained results prove the efficiency of our model which provided the prediction accuracy of 99.08% and 96.35% for the considered CT scan and X-ray datasets, respectively. Moreover, our <math><mrow><mi>U</mi> <mi>n</mi> <mi>c</mi> <mi>e</mi> <mi>r</mi> <mi>t</mi> <mi>a</mi> <mi>i</mi> <mi>n</mi> <mi>t</mi> <mi>y</mi> <mi>F</mi> <mi>u</mi> <mi>s</mi> <mi>e</mi> <mi>N</mi> <mi>e</mi> <mi>t</mi></mrow> </math> model was generally robust to noise and performed well with previously unseen data. The source code of our implementation is freely available at: https: github.com/moloud1987/UncertaintyFuseNet-for-COVID-19-Classification.