Curved bridge is commonly used in highway viaducts and overpass, on which deck pavement plays a crucial role in dispersing wheel load and providing level driving surface. Due to the influence of geometric nonlinearity of curved bridge and vehicle–bridge coupling vibration, curved bridge deck pavement (BDP) is subjected to a complex mechanical state. To study the dynamic response of the curved BDP under complex vehicle–bridge interaction (VBI) condition, this paper proposes an original dynamic analysis scheme. The BDP and bridge structure are simulated by the finite element method and the vehicle is simulated as a multi-body system (MBS); together they are integrated into a coupled system model. The numerical results are consistent with the experimental data. The dynamic responses of the proposed scheme are about 10–20% larger than those of moving constant forces, which indicates that the vehicle–bridge coupling vibration should be considered in the dynamic analysis of BDP. The parametric study shows that the vehicle weight can aggravate the response of the BDP; however, the effect of the vehicle speed on the deck pavement response and impact factor is not obvious. As road roughness classification and tire stiffness increase, the dynamic curve fluctuation of BDP is more obvious and the amplitude is larger. Through parameter sensitivity analysis, it can be concluded that vehicle weight has the greatest effect on the dynamic behavior of BDP, followed by vehicle speed and roughness, and tire stiffness has the least impact.