Most deep learning-based super-resolution (SR) methods are not image-specific: 1) They are trained on samples synthesized by predefined degradations (e.g.bicubic downsampling), regardless of the domain gap between training and testing data. 2) During testing, they super-resolve all images by the same set of model weights, ignoring the degradation variety. As a result, most previous methods may suffer a performance drop when the degradations of test images are unknown and various (i.e.the case of blind SR). To address these issues, we propose an online SR (ONSR) method. It does not rely on predefined degradations and allows the model weights to be updated according to the degradation of the test image. Specifically, ONSR consists of two branches, namely internal branch (IB) and external branch (EB). IB could learn the specific degradation of the given test LR image, and EB could learn to super resolve images degraded by the learned degradation. In this way, ONSR could customize a specific model for each test image, and thus get more robust to various degradations. Extensive experiments on both synthesized and real-world images show that ONSR can generate more visually favorable SR results and achieve state-ofthe-art performance in blind SR.