A new formula of normal contact damping for flexible joint interface was given by the revision fractal geometry theory and Hertz normal contact mechanics equation. Considering the changeable curvature radius at the tip of the summit and continuous load, the attaining way of differentiable function not partial differential function was induced to get two summits' interacting normal contact stiffness formula. The numeral curves imply that the normal contact damping decreases firstly and afterwards increases with the augment of fractal dimension of the surface raspy profile. When the fractal dimension of the coarse surface profile is smaller than the first inflection point, the normal contact damping enhances with the increase of fractal roughness. If the fractal dimension is larger than the first inflexion point, the normal contact damping reduces with the increase of fractal roughness. As the normal contact load improves, the normal contact damping firstly diminishes whereafter gains. Two inflection points and one extreme small point in the simulation curves might provide the reference for the optimization design of these contact parameters in dry tribological joint interface.