In this paper, we design a Deep Dual-Domain (D3) based fast restoration model to remove artifacts of JPEG compressed images. It leverages the large learning capacity of deep networks, as well as the problem-specific expertise that was hardly incorporated in the past design of deep architectures. For the latter, we take into consideration both the prior knowledge of the JPEG compression scheme, and the successful practice of the sparsity-based dual-domain approach. We further design the One-Step Sparse Inference (1-SI) module, as an efficient and lightweighted feed-forward approximation of sparse coding. Extensive experiments verify the superiority of the proposed D3 model over several state-of-the-art methods. Specifically, our best model is capable of outperforming the latest deep model for around 1 dB in PSNR, and is 30 times faster.