Aiming at the lack of global semantic consistency constraints and insufficient acquisition of local features of the current deep learning algorithms in the process of image restoration of broken murals， resulting in the restored murals being prone to boundary effects and blurring of details， this paper proposes a bidirectional autoregressive Transformer with fast Fourier convolutional enhancement of murals restoration method. First， a global semantic feature repair module based on the Transformer structure is designed， and an improved multi-head attention global semantic mural repair module is proposed using the bidirectional autoregressive mechanism with masked language modeling （MLM） to improve the repair capability of global semantic features. Then， a global semantic enhancement module consisting of gated convolution and a residual module is constructed to enhance the global semantic consistency constraint. Finally， the local detail repair module is designed， which adopts large kernel attention （LKA） and fast Fourier convolution （FFC） to improve the ability of capturing detailed features while reducing the loss of local detail information， so as to enhance the consistency of the local and overall features of the repaired murals. The experimental results of the digital restoration of real Dunhuang murals show that the proposed algorithm can effectively restore the structure and texture of the murals， and the subjective visual effect and objective evaluation indexes are better than the comparative algorithms.