The repairing of damaged image is an important research field in image processing.The technique of image inpainting is used widely in many fields such as repairing of damaged medical image,ancient artifact and removing of scratches and spots of dust on in film. Thiele type continued fractions interpolation function is used to interpolate pixels around damaged part of the regular texture aiming at repairing the texture based on the regular inpainting method. The mettod based on Thiele's interportion is presented. Experimental results show that the image inpainted by this method is better than the one inpainted by Photoshop. The method is an easy and effective way to repair the image.