Based on contact fractal theory and micro-contact size distribution function, a fractal model for tangential contact stiffness of joint interfaces, considering the influence of the domain extension factor for micro-contact size distribution, was proposed. By numerical simulation, the nonlinear relationship between the tangential contact stiffness and the characteristic parameters of joint interfaces was obtained. The result shows that the tangential contact stiffness of joint interfaces increases with the normal total load applied on joint interfaces, and descreases with the tangential load. Moreover, the tangential contact stiffness increases with the fractal characteristic length scale parameter G* descreasing, but complicatedly varies with the fractal dimension D.