As fractal image encoding algorithms can yield high-resolution reconstructed images at very high compression ratio, and therefore, have a great potential for improving the efficiency of image storage and image transmission. However, the baseline fractal encoding algorithm requires a great deal of time to complete the best matching search between the range and domain blocks, which greatly limits practical applications of the algorithm. In order to solve this problem, a necessary condition of the best matching search based on an image feature is proposed in this paper. The proposed method can reduce the search space significantly and excludes the most inappropriate domain blocks for each range block before carrying out the best matching search. Experimental results show that the proposed algorithm can produce good quality reconstructed images and requires much less time than the baseline encoding algorithm. Specifically, the new algorithm can speed up encoding by about 85 times with a loss of just 3 dB in the peak signal to noise ratio (PSNR), and yields compression ratios close to 34.