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In this paper, a robust fractal image compression method based on M-estimator is presented. The proposed method applies the M-estimator to the parameter estimation in the fractal encoding procedure using Huber and Tukey’s robust statistics. The M-estimation reduces the influence of the outliers and makes the fractal encoding algorithm robust to the noisy image. Meanwhile, the quadtree partitioning approach has been used in the proposed methods to improve the efficiency of the encoding algorithm, and some unnecessary computations are eliminated in the parameter estimation procedures. The experimental results demonstrate that the proposed method is insensitive to the outliers in the noisy corrupted image. The comparative data shows that the proposed method is superior in both the encoding time and the quality of retrieved images over other robust fractal compression algorithms. The proposed algorithm is useful for multimedia and image archiving, low-cost consumption applications and progressive image transmission of live images, and in reducing computing time for fractal image compression.