Dunhuang murals suffer from fading, breakage, surface brittleness and extensive peeling affected by prolonged environmental erosion. Image inpainting techniques are widely used in the field of digital mural inpainting. Generally speaking, for mural inpainting tasks with large area damage, it is challenging for any image inpainting method. In this paper, we design a multi-stage progressive reasoning network (MPR-Net) containing global to local receptive fields for murals inpainting. This network is capable of recursively inferring the damage boundary and progressively tightening the regional texture constraints. Moreover, to adaptively fuse plentiful information at various scales of murals, a multi-scale feature aggregation module (MFA) is designed to empower the capability to select the significant features. The execution of the model is similar to the process of a mural restorer (i.e., inpainting the structure of the damaged mural globally first and then adding the local texture details further). Our method has been evaluated through both qualitative and quantitative experiments, and the results demonstrate that it outperforms state-of-the-art image inpainting methods.