With influence of current, the platform and the connected riser form relative motion in the flow. In this paper, A computational fluid dynamics (CFD) model is built by strip theory and Bernoulli–Euler bending beam model. Based on this numerical model, the platform motions and corresponding current velocities are employed to investigate the responses of the riser. The numerical results indicate that the dominant crossflow and inline vibration modes are increased with the current velocity. The amplitudes of crossflow and inline vibration modes show periodic variations with the increase in the amplitude of the surge motion and the current velocity. The similar vortex shedding mode in the uniform flow is observed during vortex-induced vibrations of riser under the low frequency platform motions.