This paper is concerned with the friction and vibration characteristics of a vehicle wiper-windscreen contact. The dynamics and friction models of the wiper-windscreen system are established to study the frictional vibration and noise of the wiper-windscreen system. The dynamic model of the wiper-windscreen system is established and the analytical formulas are derived. Based on the negative slope formula of friction coefficient with respect to relative velocity, the Coulomb’s friction law, and the fluid lubrication characteristics, the friction models of the system are built in dry and wet operating conditions, respectively. Meanwhile, the formulas of friction coefficient and relative velocity in time domain are presented. The changes of blade angle and friction with time in different working conditions are investigated. The Runge-Kutta method is used to analyze the nonlinear dynamic response and friction characteristics of the friction models. The simulations successfully reproduce the vibrations of the wiper blade in actual motion. The effectiveness of the dynamic model and the friction models is verified by comparing the simulation results under different working conditions. The dynamics and friction models presented in this paper can provide theoretical references for structural optimization of the wiper blade, and thereby the vibration and noise control of the wiper-windscreen system.