Rock is a material that is affected by wear, and the curvature of the asperities on a 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 behaviour of rock joints. First, the shear stiffness formula for a joint surface is derived when the asperity curvature is constant, which shows that the shear stiffness increases with 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 a 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 increase of normal force, the higher-order asperities gradually fail 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 and a shear stiffness formula considering the change of curvature radius of the asperity is derived. The proposed model is verified on the basis of the published experimental results. The calculation results of the proposed model can reflect the test results well: for a given joint surface, with increase in normal force the joint surface gradually becomes smooth; for different joint surfaces, with increase in roughness, the joint surface is more easily smoothed.