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Image inpainting is an artistic procedure to recover a damaged painting or picture. In this paper, we propose a novel approach for image inpainting. In this approach, the Mumford-Shah (MS) model and the level set method are employed to estimate image structure of the damaged region. This approach has been successfully used in image segmentation problem. Compared to some other inpainting methods, the MS model approach can detect and preserve edges in the inpainting areas. We propose in this paper a fast and efficient algorithm which can achieve both inpainting and segmentation. In previous works on the MS model, only one or two level set functions are used to segment an image. While this approach works well on some simple images, detailed edges cannot be detected on complicated images. Although multi-level set functions can be used to segment an image into many regions, the traditional approach causes extensive computations and the solutions depend on the location of the initial curves. Our proposed approach utilizes faster hierarchical level set method and can guarantee convergence independent of initial conditions. Because we can detect both the main structure and the detailed edges, the approach can preserve detailed edges in the inpainting area. Experimental results demonstrate the advantage of our method.