The SARS-CoV-2 virus has spread worldwide, and the World Health Organization has declared COVID-19 pandemic, proclaiming that the entire world must overcome it together. The chest X-ray and computed tomography datasets of individuals with COVID-19 remain limited, which can cause lower performance of deep learning model. In this study, we developed a model for the diagnosis of COVID-19 by solving the classification problem using a self-supervised learning technique with a convolution attention module. Self-supervised learning using a U-shaped convolutional neural network model combined with a convolution block attention module (CBAM) using over 100,000 chest X-Ray images with structure similarity (SSIM) index captures image representations extremely well. The system we proposed consists of fine-tuning the weights of the encoder after a self-supervised learning pretext task, interpreting the chest X-ray representation in the encoder using convolutional layers, and diagnosing the chest X-ray image as the classification model. Additionally, considering the CBAM further improves the averaged accuracy of 98.6%, thereby outperforming the baseline model (97.8%) by 0.8%. The proposed model classifies the three classes of normal, pneumonia, and COVID-19 extremely accurately, along with other metrics such as specificity and sensitivity that are similar to accuracy. The average area under the curve (AUC) is 0.994 in the COVID-19 class, indicating that our proposed model exhibits outstanding classification performance.