Based on the fractal theory,the contact stiffness model of a single asperity at each deformation stage is obtained by taking into account the deformation state of the asperity at the four stages of elasticity,the first elastoplastic,the second elastoplastic and complete plasticity. We can obtain the related parameters that affect the normal contact stiffness of a single asperity. The frequency index is introduced and the critical value of frequency index in each deformation stage is obtained.According to the simulation results,when the fractal dimension D is set at 1. 1 ～ 1. 9,the value of dimensionless normal contact stiffness increases monotonically with the increase of D vaiue; when the frequency index of asperity is in each interval,the value of dimensionless normal contact stiffness increases with the increase of normal contact area.