Previous methods decompose blind super-resolution (SR) problem into two sequential steps: i) estimating blur kernel from given low-resolution (LR) image and ii) restoring SR image based on estimated kernel. This two-step solution involves two independently trained models, which may not be well compatible with each other. Small estimation error of the first step could cause severe performance drop of the second one. While on the other hand, the first step can only utilize limited information from LR image, which makes it difficult to predict highly accurate blur kernel. Towards these issues, instead of considering these two steps separately, we adopt an alternating optimization algorithm, which can estimate blur kernel and restore SR image in a single model. Specifically, we design two convolutional neural modules, namely Restorer and Estimator. Restorer restores SR image based on predicted kernel, and Estimator estimates blur kernel with the help of restored SR image. We alternate these two modules repeatedly and unfold this process to form an end-to-end trainable network. In this way, Estimator utilizes information from both LR and SR images, which makes the estimation of blur kernel easier. More importantly, Restorer is trained with the kernel estimated by Estimator, instead of ground-truth kernel, thus Restorer could be more tolerant to the estimation error of Estimator. Extensive experiments on synthetic datasets and real-world images show that our model can largely outperform state-of-the-art methods and produce more visually favorable results at much higher speed. The source code is available at https://github.com/greatlog/DAN.git.