In view of the drawback of most image inpainting algorithms by which texture was not prominent, an adaptive inpainting algorithm based on continued fractions was proposed in this paper. In order to restore every damaged point, the information of known pixel points around the damaged point was used to interpolate the intensity of the damaged point. The proposed method included two steps; firstly, Thiele's rational interpolation combined with the mask image was used to interpolate adaptively the intensities of damaged points to get an initial repaired image, and then Newton-Thiele's rational interpolation was used to refine the initial repaired image to get a final result. In order to show the superiority of the proposed algorithm, plenty of experiments were tested on damaged images. Subjective evaluation and objective evaluation were used to evaluate the quality of repaired images, and the objective evaluation was comparison of Peak Signal to Noise Ratios (PSNRs). The experimental results showed that the proposed algorithm had better visual effect and higher Peak Signal to Noise Ratio compared with the state-of-the-art methods.