The current-carrying friction of electric railway arch system seriously affects the life of pantograph slide and catenary wire and the quality of electric locomotive. The contact surface will deform with the change of running time, which seriously affects the friction of contact surface. In order to model the current friction force of the wire mesh, this paper uses the sliding electric contact experimental machine developed by ourselves to simulate the contact state of the high-speed railway pantograph and catenary, analyzes the influencing factors of the friction force and conducts modeling research. Firstly, through theoretical analysis of the influencing factors of friction, a mathematical model of each influencing factor and friction coefficient is established based on the experimental results, which is combined with the Dahl friction model in the time domain and the effective parameter identification of the model is carried out by using the Grey Wolf optimization algorithm. Finally, the frictional model of the arch mesh with regard to the acting time is established. Finally, the validity of the model is verified by the experimental results, which provides a reference for the further study of the friction force of the arch mesh system in the future.