Lung diseases caused by fungal or bacterial infections can lead to inflammation in lung and even death when not detected early. A standard method for diagnosing lung diseases is the use of chest X-ray, which require careful examination of X-ray images by a radiology expert. Therefore, this study proposes several new architecture models, namely CSLNet, to classify chest X-ray images for diagnosing whether patients suffer from COVID-19, viral pneumonia, bacterial pneumonia, tuberculosis, and normal. The experimental results show that the model has an 0.99 average Accuracy, 0.98 Precision, 0.98 Recall, and 0.98 f1-score. Meanwhile, the Receiver Operating Characteristic (ROC) for bacterial pneumonia, COVID-19, normal, tuberculosis, and viral pneumonia are 0.97, 0.99, 0.99, 0.94, and 0.97 respectively. This study is based on a deep learning with a new model, CSLNet, which can work well on the dataset of chest X-ray images used for diagnosing lung diseases.