Different from the object motion blur, the defocus blur is caused by the limitation of the cameras' depth of field. The defocus amount can be characterized by the parameter of point spread function and thus forms a defocus map. In this paper, we propose a new network architecture called Defocus Image Deblurring Auxiliary Learning Net (DID-ANet), which is specifically designed for single image defocus deblurring by using defocus map estimation as auxiliary task to improve the deblurring result. To facilitate the training of the network, we build a novel and large-scale dataset for single image defocus deblurring, which contains the defocus images, the defocus maps and the all-sharp images. To the best of our knowledge, the new dataset is the first large-scale defocus deblurring dataset for training deep networks. Moreover, the experimental results demonstrate that the proposed DID-ANet outperforms the state-of-the-art methods for both tasks of defocus image deblurring and defocus map estimation, both quantitatively and qualitatively. The dataset, code, and model is available on GitHub: https://github.com/xytmhy/DID-ANet-Defocus-Deblurring.