<p>Graph neural networks (GNNs) have shown significant success in graph representation learning, which depends on a credible graph structure. However, labeling the graph structure is difficult in real applications, which brings a crucial problem in graph representation learning with a noisy graph structure. To address this issue, in this paper, we propose a progressive graph structure denoising framework, a novel architecture that melds the strengths of progressive refinement with residual learning. Firstly, we design a novel attention-based twisted graph convolutional layer (ATGCL) to learn the residuals of both node representation and adjacency matrix, which can effectively reduce the noise and restore the graph structure in the graph and promote more accurate node representation. Then, we utilize ATGCL as the backbone to construct a Deep denoising graph neural network (DDGNN) to overcome the well-known problem of over-smoothing, where the learned residuals are applied to the previous node representation and adjacency matrix in each layer. By the benefit of progressive optimization, the noisy graph structure can be well refined. The experiment results reveal that in semi-supervised node classification tasks, our method achieves competitive classification accuracy on three widely used datasets. In addition, we conduct extensive experiments on graph data with noisy graph structure, which further demonstrate the effectiveness and robustness of our proposed DDGNN.</p>