<p>This paper studies the coupled cross-flow and in-line vibration characteristics of marine catenary composite riser under the combined action of gas-liquid multiphase internal flow, external ocean currents and composite material anisotropy. Based on Hamilton’s variational principle, the coupled vibration control equations of composite marine catenary riser in cross-flow and in-line directions were established considering the combined action of gas-liquid multiphase internal flow, external ocean currents and composite material anisotropy. The van der Pol wake oscillator model was used to simulate the flow force of the ocean current in the cross-flow and in-line directions of the slender riser. Newmark-β and fourth-order Runge-Kutta methods were used to solve the coupled dynamics equation. The research results show that gas volume fraction and fiber orientation angle significantly suppress structural mode of vibration, while liquid flow rate exhibits mode of vibration excitation effects. Increasing fiber orientation angle reduces vibration displacement and enhances motion periodicity, whereas higher liquid velocities induce chaotic system behavior. Bending stress shows nonlinear sensitivity to low gas fractions and liquid velocity changes, exhibiting stress transitions. These findings provide critical insights for optimizing composite riser design and safety in deep-sea energy extraction, highlighting parameter-specific control strategies for vibration mitigation and stress management under complex multiphase flow conditions.</p>