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 an attention regularized 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 handcrafted 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 the outputs of two branches. The proposed Thorax-Net model has been evaluated against three state-of-the-art deep learning models using the patient-wise official split of the Chest X-ray 14 dataset and against other five deep learning models using the image-wise random data split. Our results show that Thorax-Net achieves an average per-class 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 trained without using external data.