In various plastic forming processes of metals, friction has been revealed to play an important role in the determination of the material flow, fracture, and surface quality. The precise description of friction behavior is thus a critical issue for the accurate prediction and analysis of these formability indicators. Generally, the friction behavior is inevitably affected by material hardening and junction growth. However, few of the previous models have taken both of them into consideration, especially for the nonlinear hardening materials. In this study, the classical contact model was modified to include the power-law hardening material, and the general friction law combined with Tabor's equation was employed to estimate the friction stress with the junction growth of asperities. An asperity-based friction model for rough surfaces in metal forming process was then obtained by summarizing the normal and tangential stresses of all the asperities on the surface using Greenwood and Williamson (GW) method. The model was validated by comparing to the finite element (FE) results and the experimental results. And its comparison with Kogut and Etsion (KE) model and Cohen's model revealed a wider range of application for the present model. It was also found to be able to predict the friction coefficient and the real contact area of nonlinear hardening materials under various contact conditions. This work is helpful to understand the friction behavior and further guide the simulation and optimization of forming processes.