To better understand the fractal characteristics of coal fracture network and find the relation between 2D and 3D fractal dimensions, the improved box counting method was utilized to calculate 2D and 3D fractal dimensions based on high resolution CT images of 4 coal samples (R-o from 2.915% to 4.69%). Based on the calculated 2D and 3D fractal dimension, the size of representative element volume (REV), the relationship between D-f2 and D-f3 and the relationship between porosity and fractal dimension were investigated extensively. As the complement of previous theoretical studies, the exponential relationship between porosity and fractal dimension was proved. By deducing formulas based on fractal theory, the ratio of the minimum pore size to the maximum pore size could be obtained. Evidently, the relation between 2D and 3D fractal dimension of coal could be expressed as D-f3 = CDf2 + 1, and the slope of the line, C, depends on the average 2D fractal dimension of the sample.