Vortex-induced vibration is one of the main causes of fatigue failure of marine risers. The cross-flow vortex-induced vibration characteristics of marine risers under the combined action of gas-liquid two-phase internal flow and uniform external flow are analyzed and studied.The nonlinear dynamic control equations for the top-tensioned riser are established.The improved wake oscillator model is applied, and the nonlinear equations are rendered dimensionless.The Galerkin method is utilized to discretize both the riser control equations and the wake oscillator equations. The fourth-order Runge-Kutta method is then employed to solve these equations. The vortex-induced vibration characteristics of the top-tensioned riser under various internal flow velocities and gas volume fractions are investigated. Through a comparison between the numerical results and the experimental data, the accuracy of the model is validated.The results indicate that the dominant mode of the marine riser's vortex - induced vibration response is chiefly determined by the velocity of the external ocean current. Specifically, the greater the external flow velocity, the higher the excited dominant mode. Both the internal flow velocity and the gas volume fraction have an impact on the natural frequency of the riser. As the gas volume fraction increases, the natural frequency of the riser becomes higher. Conversely, as the internal flow velocity increases, the natural frequency of the riser decreases.