Deep learning techniques have been increasingly used to provide more accurate and more accessible diagnosis of thorax diseases on chest radiographs. However, due to the lack of dense annotation of large-scale chest radiograph data, this computer-aided diagnosis task is intrinsically a weakly supervised learning problem and remains challenging. In this paper, we propose a novel deep convolutional neural network called Thorax-Net to diagnose 14 thorax diseases using chest radiography. Thorax-Net consists of a classification branch and an attention branch. The classification branch serves as a uniform feature extraction-classification network to free users from the troublesome hand-crafted feature extraction and classifier construction. The attention branch exploits the correlation between class labels and the locations of pathological abnormalities via analyzing the feature maps learned by the classification branch. Feeding a chest radiograph to the trained Thorax-Net, a diagnosis is obtained by averaging and binarizing the outputs of two branches. The proposed Thorax-Net model has been evaluated against three state-of-the-art deep learning models using the patientwise official split of the ChestX-ray14 dataset and against other five deep learning models using the imagewise random data split. Our results show that Thorax-Net achieves an average per-class area under the receiver operating characteristic curve (AUC) of 0.7876 and 0.896 in both experiments, respectively, which are higher than the AUC values obtained by other deep models when they were all trained with no external data.