In the current structure-based image inpainting algorithm,the Fast Marching Method can simply and rapidly repair the damaged region in the digital image.However,the effect is not very good,especially poor to preserve the edge information.By introducing the gradient function and the distance weight function,an improved algorithm has been proposed,which sorts the neighboring points with weight to repair the damaged region and uses the gradient-sorting estimation to preserve the edge.The results of experiments have indicated that the improved one is better.The gradient function and the distance weight function can make results more better.