In fractal image coding, optimal contractive mapping should be determined to minimize the difference between the original image and a reconstruction of it. Though this can be determined by an exhaustive search, this approach is impractical because of its heavy calculation cost. Therefore, to reduce calculation cost, conventional methods determine an suitable contractive mapping by minimizing the difference between the original image and the collage. However, the obtained mapping cannot necessarily reconstruct a high quality image and this does not minimize reconstruction errors. Hence, in order to always obtain high-quality reconstructed images, we propose a new fractal image coding to minimize the errors by using genetic algorithms.