The purpose of this study was to evaluate the diagnostic performance achieved by using fully-connected small artificial neural networks (ANNs) and a simple training process, the Kim-Monte Carlo algorithm, to detect the location of pneumothorax in chest X-rays. A total of 1,000 chest X-ray images with pneumothorax were taken randomly from NIH (the National Institutes of Health) public image database and used as the training and test sets. Each X-ray image with pneumothorax was divided into 49 boxes for pneumothorax localization. For each of the boxes in the chest X-ray images contained in the test set, the area under the receiver operating characteristic (ROC) curve (AUC) was 0.882, and the sensitivity and specificity were 80.6% and 83.0%, respectively. In addition, a common currently used deep-learning method for image recognition, the convolution neural network (CNN), was also applied to the same dataset for comparison purposes. The performance of the fully-connected small ANN was better than that of the CNN. Regarding the diagnostic performances of the CNN with different activation functions, the CNN with a sigmoid activation function for fully-connected hidden nodes was better than the CNN with the rectified linear unit (RELU) activation function. This study showed that our approach can accurately detect the location of pneumothorax in chest X-rays, significantly reduce the time delay incurred when diagnosing urgent diseases such as pneumothorax, and increase the effectiveness of clinical practice and patient care.