As an integral component of blind image deblurring, non-blind deconvolution removes image blur with a given blur kernel, which is essential but difficult due to the ill-posed nature of the inverse problem. The predominant approach is based on optimization subject to regularization functions that are either manually designed or learned from examples. Existing learning-based methods have shown superior restoration quality but are not practical enough due to their restricted and static model design. They solely focus on learning a prior and require to know the noise level for deconvolution. We address the gap between the optimization- and learning-based approaches by learning a universal gradient descent optimizer. We propose a recurrent gradient descent network (RGDN) by systematically incorporating deep neural networks into a fully parameterized gradient descent scheme. A hyperparameter-free update unit shared across steps is used to generate the updates from the current estimates based on a convolutional neural network. By training on diverse examples, the RGDN learns an implicit image prior and a universal update rule through recursive supervision. The learned optimizer can be repeatedly used to improve the quality of diverse degenerated observations. The proposed method possesses strong interpretability and high generalization. Extensive experiments on synthetic benchmarks and challenging real-world images demonstrate that the proposed deep optimization method is effective and robust to produce favorable results as well as practical for real-world image deblurring applications.