Riser is a weak point during deepwater drilling process,and its transverse vibration will lead to various failures such as eccentric wear,breakdown and collapsing,et al. The study of transverse vibration lays on a theoretical foundation for the choice of deepwater drilling parameters and design for well drilling and completion, which will increase the security of risers. In this paper, the deepwater riser is simplified as a EulerBernoulli beam with large deformation straindisplacement equation and elastic boundary condition, and a mathematic model is deduced for the deepwater riser under coupling force of wave and current by using Hamilton′s principle. The nonlinear dynamic equation describes the transverse vibration of deepwater riser under drilling condition. Galerkin method and numerical analysis are then used to find out the stability mechanism of transverse vibration. The analysis above shows that the multiple values and jump phenomenon exist in the main resonance process. The response amplitude raises when the ratio D/τ between diameter and thickness of the riser increases. The bandwidth broadens and unsteady region extends as the ratio H/T between wave effective height and period increases. The response amplitude of jump phenomenon becomes more obvious with the increase of ratio l/H between riser length and wave height. The deepwater riser system experiences alternate change of periodic motion and chaotic movement when the wave period varies from 3s to 10s,and simultaneously,there are evident perioddoubling bifurcation windows.