To predict the peak signal-to-noise ratio (PSNR) quality of decoded images in fractal image coding more efficiently and accurately, an improved method is proposed. After some derivations and analyses, we find that the linear correlation coefficients between coded range blocks and their respective best-matched domain blocks can determine the dynamic range of their collage errors, which can also provide the minimum and the maximum of the accumulated collage error (ACE) of uncoded range blocks. Moreover, the dynamic range of the actual percentage of accumulated collage error (APACE), to , can be determined as well. When reaches a large value, such as 90%, to will be limited in a small range and APACE can be computed approximately. Furthermore, with ACE and the approximate APACE, the ACE of all range blocks and the average collage error (ACER) can be obtained. Finally, with the logarithmic relationship between ACER and the PSNR quality of decoded images, the PSNR quality of decoded images can be predicted directly. Experiments show that compared with the previous similar method, the proposed method can predict the PSNR quality of decoded images more accurately and needs less computation time simultaneously.