When pathogens such as viruses, bacteria and fungi attack the lungs, the alveoli fill with in-flamed fluid, causing pneumonia. Early diagnosis of this disease, which has fatal outcomes especially in children under 5 years old, is very important in controlling undesirable situations. Chest X-ray images play an important role in the diagnosis of pneumonia. In addition, the fact that the amount of radiation is lower than imaging devices such as tomography and the possibility of being accessible even from rural areas creates an advantage for X-ray devices. However, X-ray images that are not always clear or human conditions such as fatigue and lack of attention can make it difficult for specialists to detect pneumonia. In this study, a transfer learning-based convolutional neural network (CNN) approach is proposed, which can help specialists in the early and accurate diagnosis of pneumonia in children and, classify healthy and diseased individuals through Chest X-ray images. As a result of the study, an original CNN was proposed by adding additional layers to the AlexNet architecture layers and a test accuracy of 96.31% was obtained.