Rock is a wearable material, the curvature of the asperities on rock joint surface increases with the degree of wear after shearing. Based on the Greenwood and Williamson (GW) model, a new model considering the change of asperity curvature is proposed to explain the wear behavior of rock joints. Firstly the shear stiffness formula of the joint surface is derived when the asperity curvature is constant, which shows that the shear stiffness increases with the increase of asperity curvature. According to the Mohr-Coulomb criterion, the yield position of a single asperity under normal force and tangential friction force is discussed. Then, the critical normal force for a single asperity at specific friction coefficient is obtained, which shows that the normal force corresponds to the curvature radius of the asperity. A rough surface model with multi-level curvature radius is proposed. With the increase of normal force, the higher-order asperities gradually failure and the curvature radius become larger. A specific pressure value excites a specific radius of curvature, and the larger the pressure, the larger the radius of curvature. The relation between the normal force and the curvature radius is proposed. Then the shear stiffness formula considering the change of the curvature radius of the asperity is derived. Based on the published experimental results, the rationality of the proposed model is verified. The calculation results of the proposed model can well reflect the test results: for the given joint surface, with the increase of normal force, the joint surface gradually becomes smooth; for different joint surfaces, with the increase of roughness, the joint surface is easier to be smoothed.