In this study, an Euler–Lagrange coupling two-phase flow model, namely movable bed simulator (MBS)-two-dimensional (2D) model was employed to explore the current-induced live-bed scour beneath marine pipelines. The fluid phase characteristics, such as velocity and pressure, were obtained by the Reynolds-averaged Navier–Stokes (RANS) equations with a k-ε turbulence closure model in a two-dimensional Eulerian grid, whereas the seabed beneath pipelines was traced as an assembly of discrete sand grains from the Lagrangian point of view. The live-bed scour was evolved as the motion of a granular media based on distinct element method (DEM) formulation, in which the frequent interparticle collision was described with a spring and dashpot system. The fluid flow was coupled to the sediment phase, considering the acting drag forces between. Comparison between the numerical result and experimental measurement confirms that the numerical model successfully estimates the bed profile and flow velocity field. It is evident that the fluid shear stress decreases with the increasing of gap ratio e/D. The numerical model provides a useful approach to improve mechanistic understanding of hydrodynamic and sediment transport in live-bed scour beneath a marine pipeline.