A new method for fractal image compression by applying Jacquin's algorithm to a polyphase decomposed image is proposed to increase the encoding efficiency in this research. By using a (P X P) : (1 X 1) polyphase decomposition with P equals 2n, we divide an image into P X P subimages and then apply the Jacquin compression algorithm to these subimages independently. We show that the resulting scheme can improve the coding speed by a factor of P2 at the sacrifice of the decompressed image quality. Besides, since the subimages are very similar to each other, we may focus on a small subset of subimages, seek the appropriate domain block for their range blocks, and record the information of address mapping, scaling and offset. To encode the remaining subimages, we simply determine the scaling and the offset based on the same set of addressing mapping previously found. A set of numerical experiments with various parameters, including the polyphase decimation factor P, the size D (or R) of domain (or range) blocks, and the size s of search step, are performed to illustrate the tradeoff between the speed, image quality, and compression rate.