This study aims to develop a modularized simulation system to estimate dynamic responses of floating Offshore Wind Turbines (OWTs) based on the concepts of spar buoy and Tension Leg Platform (TLP) corresponding with two typical mooring lines. The modular system consists of the hydrodynamic simulator based the Cummins time domain equation, the Boundary Element Method (BEM) solver based on the 3D source distribution method, and an open-source visualization software ParaView to analyze the interaction between floating OWTs and waves. In order to realize the effects of mooring loads on the floating OWTs, the stiffness and damping matrices are applied to the quasi-static mooring system. The Response Amplitude Operators (RAOs) are compared between our predicted results and other published data to verify the modularized simulation system and understand the influence of mooring load on the motion responses in regular or irregular waves. It is also demonstrated that the quasi-static mooring system is applicable to different types of mooring lines as well as determining real-time motion responses. Eventually, wave load components at the resonance frequencies of different motion modes for selected floating OWTs would be present in the time domain.