Dunhuang mural images have complex line texture structure and missing contour edges,There are structure propagation errors and block effects when using Criminisi algorithm to inpainting. Therefore, a mural image inpainting algorithm based on edge missing structure reconstruction and improved priority is proposed in this paper. First, the missing edge contour of the damaged mural is reconstructed by adaptive Bézier curve fitting method to enhance the structure of the mural and guide the image restoration. Then, the prior information of local features such as gradient and curvature is introduced to improve the priority function, which makes the calculation of priority more reasonable and avoids the problem of wrong filling caused by the priority frequently tends to 0. Finally, the sequential similarity detection algorithm based on dynamic threshold is used for searching matching blocks, which improves the efficiency of mural repair, and the mural image inpainting is completed iteratively. The experimental results of digital inpainting of real Dunhuang murals show that the algorithm can solve the problems of structure propagation error and block effect of Criminisi algorithm, and the subjective and objective evaluation results of inpainting murals is better than other comparative algorithms.