Fractal image coding based on Iterated Function System (IFS) has been attracting much interest because of possibilities of drastic data compression. It achieves compression by using the self-similarity in an image. It is one of the weak points on IFS that the calculation time is huge. Especially, the amount of calculation on scaling parameter and rmse is very huge. In this paper, we propose two schemes to reduce the calculation time while the quality of the image is kept. The first one reduces calculation time of parameters, affine transform and rmse by using the maximum amplitude ratio which is a ratio between the maximum amplitude range of range block and that of domain block. By using the maximum amplitude radio, domain block which does not seem to choose is excluded before calculating parameters. The second one reduces calculation time of scaling parameters by using the ratio between variance of range block and that of domain block. The variance ratio is used instead of the scaling parameter. We perform the fractal compression experiments based on the proposed scheme to verify the effectiveness of these schemes. Computational experiments show that about 50% of calculation time is reduced by using both of two schemes.