Based on the three-dimensional fractal theory, a fractal model of normal contact stiffness and contact damping of joint surfaces considering simultaneously the influence of the friction and the asperity interaction was established. Through the simulation of the built model, the influence of friction coefficient, fractal dimension, fractal roughness parameter and contact load on contact stiffness and contact damping was analyzed. The results show that the contact stiffness and contact damping of this model increase with the increase of normal load and fractal dimension, and decrease with the increase of the fractal roughness parameter; and the contact stiffness decreases with the increase of friction coefficient, but contact damping increases first and then decreases with the increase of friction coefficient. In addition, the cases of interaction only considering the asperity and interaction without the friction and the asperity are compared and analyzed, and it is concluded that the interaction of asperities can slightly increase the contact stiffness when the fractal dimension D=2.4, and at that time D≥2.5, the asperity interaction can reduce the contact stiffness, and the degree of reduction can become larger and larger. At that time2.4≤D≤2.9, the asperity interaction can reduce the contact damping. In addition, the simulation calculation results of the built model are compared with the experimental data to verify the correctness of the built model.