Knee osteoarthritis (OA) is one of the most common musculoskeletal disorders and requires early-stage diagnosis. Nowadays, the deep convolutional neural networks have achieved greatly in the computer-aided diagnosis field. However, the construction of the deep learning models usually requires great amounts of annotated data, which is generally high-cost. In this paper, we propose a novel approach for knee OA diagnosis, including severity classification and lesion localization. Particularly, we design a self-ensembling framework, which is composed of a student network and a teacher network with the same structure. The student network learns from both labeled data and unlabeled data and the teacher network averages the student model weights through the training course. A novel attention loss function is developed to obtain accurate attention masks. With dual-consistency checking of the attention in the lesion classification and localization, the two networks can gradually optimize the attention distribution and improve the performance of each other, whereas the training relies on partially labeled data only and follows the semi-supervised manner. Experiments show that the proposed method can significantly improve the self-ensembling performance in both knee OA classification and localization, and also greatly reduce the needs of annotated data.