Among radiological imaging data, chest X-rays are of great use in observing COVID-19 mani- festations. For mass screening, using chest X-rays, a computationally efficient AI-driven tool is the must to detect COVID-19 positive cases from non-COVID ones. For this purpose, we proposed a light-weight Convolutional Neural Network (CNN)-tailored shallow architecture that can automatically detect COVID-19 positive cases using chest X-rays, with no false positive. The shallow CNN-tailored architecture was designed with fewer parameters as compared to other deep learning models, which was validated using 130 COVID-19 positive chest X-rays. In this study, in addition to COVID-19 positive cases, another set of non-COVID-19 cases (exactly similar to the size of COVID-19 set) was taken into account, where MERS, SARS, Pneumonia, and healthy chest X-rays were used. In experimental tests, to avoid possible bias, 5-fold cross validation was followed. Using 260 chest X-rays, the proposed model achieved an accuracy of an accuracy of 96.92%, sensitivity of 0.942, where AUC was 0.9869. Further, the reported false positive rate was 0 for 130 COVID-19 positive cases. This stated that proposed tool could possibly be used for mass screening. Note to be confused, it does not include any clinical implications. Using the exact same set of chest X-rays collection, the current results were better than other deep learning models and state-of-the-art works.