A new tangential contact model between a rough surface and a smooth rigid flat is proposed in this paper. The model considers the contribution of both elastically deformed asperities and plastically deformed asperities to the total tangential load of rough surface. The method combining the Mindlin partial slip solution with the Hertz solution is used to model the contact formulation of elastically deformed asperities, and for the plastically deformed asperities, the solution combining the fully plastic theory of normal contact with the bi-linear relation between the tangential load and deformation developed by Fujimoto is implemented. The total tangential contact load is obtained by GW statistical analysis procedure. The proposed model is first compared to the model considering only elastically deformed asperities, and the effect of mean separation and plasticity index on the relationship between the tangential load and deformation is also investigated. It is shown that the present model can be used to describe the stick-slip behavior of the rough surface, and it is a more physics-based model for the tangential rough contact. A comparison with published experimental results is also made. The proposed model agrees very well with the experimental results when the normal load is small, and shows an error when the normal load is large.