The dynamic response of a floating wind turbine with 5-megawatt power and large size undergoing different ocean waves is examined by the numerical simulations based on a modified approach which combines the 3D flexible catenary theory with the finite element method. By use of our modified approach, the additional mooring dynamic behaviors including the structural inertial effect and fluid drag, compared to the previous quasi-static model, are involved in this study; what’s more, the integrated system of which the dynamic interaction between the flexible components such as blades, tower, SPAR platform and catenary mooring system is considered too. The influences of catenary mooring-line inertia and fluid damping force on tension and motion characteristics of catenary mooring system are presented, and the impact of mooring-line dynamics on the integrated system of wind turbine response is studied and compared with the quasi-static method which only includes the static restoring force of the catenary. Our numerical results show that the dynamic characteristics of mooring-line may significantly increase the top tension, particularly, the peak-trough tension difference of snap tension may be more than 10 times larger than the quasi-static result owing to the occurrence of taut-slack during the dynamic response on certain situations. When the wave frequency is much higher than the system, the dynamic effects of the mooring system will accelerate the decay of transient items of the dynamic response; when the wave frequency and the system frequency are close to each other, the dynamic characteristics of mooring systems can significantly reduce the response displacement of the floating SPAR, i.e. the amplitude is reduced by 20%.