Due to the great damage to widely utilized flexible structures in ocean engineering, vortex-induced vibration (VIV) of such long flexible marine structures is still a hot issue that needs more theoretical research, and CFD techniques become gradually indispensable to study the VIV problem. In this paper, two-dimensional Reynolds-averaged Navier-Stokes (RANS) equations are adopted to investigate transverse VIV of elastically mounted rigid cylinder with low mass-damping, and two typical turbulent models are applied to solve the RANS equations: RNG k-ε model and SST k-ω model. By comparing the cylinder displacement response and vortex shedding modes of three different response branches, analysis of differences between two turbulence models are presented. The numerical results indicate that SST k-ω model is more appropriate for VIV of the elastically mounted rigid cylinder. Subsequently, other hydrodynamic coefficients obtained by SST k-ω model are discussed and compared with previous research in detail. This investigation provides theoretical evidence for the numerical simulation of VIV of marine riser in engineering application.