This paper presents a nonlinear vehicle-road coupled model which is composed of a seven-degree of freedom (DOF) vehicle and a simply supported double-layer rectangular thin plate on a nonlinear viscoelastic foundation. The nonlinearity of suspension stiffness, suspension damping and tire stiffness is considered and the Leaderman constitutive relation and Burgers model are applied to describe the nonlinear and viscoelastic properties of the asphalt topping material. The equations of motion for the vehicle-road system are derived and the partial differential equation of road pavement is discretized into an infinite number of second-order ordinary differential equations and first-order ordinary differential equations by Galerkin’s method and a mathematic transform. A numerical integration method for solving this coupled system is developed and the nonlinear dynamic behaviors of the system are analyzed. In addition, the simulation results of the coupled model are compared to those of the uncoupled traditional model. It is found that with the increase of harmonic road surface roughness amplitude, the vehicle body’s vertical response is always periodic, whereas the pavement’s response varies from quasi-periodic motion to chaotic motion. In the case of a heavy-duty vehicle, a soft subgrade or a higher running speed, the application of the proposed nonlinear vehicle-road coupled model would bring higher computational accuracy and make it possible to design the vehicle and pavement simultaneously.