Abstract: Based on the equations of vortex-induced oscillation of tension legs, the effect of parametric excitation frequency on the first-order dynamic response of a tension legwas investigated by considering the non-linear fluid damping and parametric excitation. In the investigation, the Galerkin method and the numerical integration were used. Numerical relationships between displacement response, dynamic moment and dynamic shearing force and parametric excitation frequencywere obtained. The calculated result shows that the displacement response and the dynamic moment at mid-span both reach their maximums when the parametric excitation frequency is twice as large as the first-order natural frequency of a tension leg.