Based on the fractal theory and Hertz contact theory,the establishment of fractal model for tangential stiffness for contact surface of cylindrical gear with variable hyperbolic circular-arc-tooth-trace（ VH-CATT） is presented. This model is obtained by introducing the equation of critical contact area of elastic and plastic deformation of asperity and employing the surface contact coefficient of two ellipsoids to modify the asperity distribution function. The rationality of the surface contact coefficient is proved by numerical simulation,and the influence of the main parameters（ such as normal load,fractal dimension,roughness amplitude,tangential load,material propertied parameters） on the tangential stiffness is analyzed. The results are as follows,the normal load is proportional to the tangential stiffness,but when the fractal dimension is not the same,there is a big difference between them. The tangential stiffness first increases and then decreases with the increasing of the fractal dimension,and reaches the maximum when the fractal dimension is 1. 85. The tangential stiffness decreases with the increasing of the roughness amplitude and the tangential load,and increases with the increasing of the material propertied parameters. The model provides a theoretical basis for the further study of the tangential stiffness for contact surface of VH-CATT.