According to the appearance of fractal feature degeneration during fractal morphing, a new feature corresponding method based on local attractor’s approximate convex hull (LAA) and revolving matching method (RMM) is introduced. The local attractor, part of the whole IFS attractor, is indicated by an independent IFS code, whose internal contractive affine transformations have unique fixed points, and the LAA is constructed by contouring the convex hull of all the fixed points of the IFS. It is proved that the similarity between different IFS’s LAAs is equivalent to the similarity of its local attractors, so the feature corresponding can be built upon the LAAs. The matching between two LAAs is based on RMM and the matching order is restricted clockwise or anticlockwise. Then, the feature corresponding between two IFS’s local attractors is determined by searching for the most similar matching of the LAAs. Finally, the parameters of the iterated function are linearly interpolated to finish the morphing procedure of two IFS’s fractal attractors and to perform the fractal morphing with fractal feature preserved.