The semi-empirical Kozeny-Carman (KC) equation，the most well-known permeability-porosity relation, is widely used in the field of seepage flow in porous media. However, the physical mechanisms behind the empirical KC constant are not clear, and the KC constant has not been proved to be a constant. The fractal scaling laws of pores have been extensively found in porous media. Therefore, the effective permeability of homogenous porous media is presented and the analytical expression of KC constant is derived based on the fractal characteristics of porous media and the microcosmic geometrical model. The results indicate that the fractal analytical expression of KC constant depends on the micro-structure of porous media. As a function of porosity and fractal dimensions, KC constant increases with the increase of porosity.