Fractal dimensions of a terrain quantitatively describe the self-organized structure of the terrain geometry. However, the local topographic variation cannot be illustrated by the conventional box-counting method. This paper proposes a successive shift box-counting method, in which the studied object is divided into small sub-objects that are composed of a series of grids according to its characteristic scaling. The terrain fractal dimensions in the grids are calculated with the successive shift box-counting method and the scattered points with values of fractal dimensions are obtained. The present research shows that the planar variation of fractal dimensions is well consistent with fault traces and geological boundaries.