Correct estimation of fracture permeability is a key factor for the successful development of fractured reservoir. Based on the Kozeny-Carman equation, we have described the deviation from the conventional cubic law of the fracture permeability by using a fractal model of fracture surfaces. In order to confirm the validity of the description, we carried out several laboratory experiments and numerical simulations to the artificially prepared fracture specimens whose geometric surface properties were controlled by the fractal model. Consequently, the validity was confirmed and it was cleared that the two-dimensional tortuosity and the shape factor affect on the deviation from the cubic law more remarkably than the fractal dimension and the steepness, and therefore, these parameters are very important to estimate the deviation from the cubic law of fracture permeability correctly. Furthermore, it was cleared that fluids flow through a fracture with selecting the large aperture regions and the tortuosity increases with increase in the contact area of the fracture.