Abstract: Observations were made on natural coal and rock samples by X-ray tomography to examine the multi-scale anisotropic characteristics of fractures. Canny edge detector and directional line detectors were employed to segment the CT images. As a result, the overall features, the horizontal and the vertical features of the macro-and mini-fractures were extracted, from which the overall and anisotropic fractal dimensions and porosities, as well as its 3D distribution, were calculated. In addition, the relationship among fractal dimension, porosity and permeability, together with its extrapolation to real engineering rock mass, were discussed. The study showed that the fractal dimensions and porosities were different with variations of the scanning sections, and with different directions of same section for the coal and rock samples. Detailed descriptions were made in 2D and 3D space on anisotropic features, porosity and permeability for coal and rocks.