In Fractal image coding (FIC), a parti-tioning of the original im age into ranges and domains is required, which greatly afects the coding performance. Usually, the more adaptive to the image content the partition is, the higher performance it can achieve. Nowadays, some alleged Region-based fractal coders (RBFC) using split-and-merge strategy can achieve better adaptivity and perform ance com pared with traditional rectangular block partitions. However, the regions are still with linear con. tour. In this paper, we present a Freely-shaped Region-based fractal coder rFs. (RBFC) using a two-step partitioning, i. e. coarse partitioning bas ed on fractal dim ension and fine partitioning based on region growth, which brings freely-shaped regions. Our highly im age-adaptive scheme can achieve better rate. distortion curve than conventional scheme, even more visually pleasing resultsat the same perform ance.