In this paper we propose a method that improves PSNR at low bit rate and reduces computational complexity in fractal image coding based on discrete wavelet transform. The proposed method, which uses significant coefficient tree, improves PSNR of the reconstructed image and reduces computational comlexity of mapping domain block onto range block by matching only the significant coefficients of range block to coefficients of domain block. Also, the proposed method reduces error propagation form lower resolution subbands to higher resolution subbands by correcting error of lower resolution subbands. Some experimental results confirm that the proposed method reduces encoding and decoding time significantly and has fine reconstructed images having no blocking effect and clear edges at low bit rate.