Riser vortex-induced vibration (VIV) has been the outstanding problem affecting the normal safe operation in offshore oil exploitation. In this paper, based on computational fluid dynamics, a three-dimensional large eddy simulation (LES) numerical model was used to calculate the flow fields of unsteady flow around marine riser with different approaching flow velocities. Then streamlines, velocity and vorticity contours, drag and lift coefficients in different conditions were obtained. Simulation results indicate that the flow properties in different depth display obvious difference, which present complex three dimensional characteristics with interacting. It is thus clear that flow around marine riser can not be regarded as plane potential flow simply. The results also show that with larger approaching flow velocity, lift coefficient amplitude is bigger and frequency is higher, which is easier to result in vibration. Our approach may provide some references for safe design and engineering practice of VIV controlling of marine riser.