Capable of capturing offshore wind energy， the floating wind turbine is one of the primary research interests for research ers in the wind energy community. Researchers usually adopt two-dimensional low-degree-of-freedom simplified planar models for offshore barge-type wind turbines， where the model parameters are identified by the nonlinear least square method. In this case， the accuracy of these models depends highly on parameter fitting. Given the unique structure of offshore floating wind turbines and the surrounding environment， a multi-degree-of-freedom coupled dynamical model is necessary to yield more realistic dynamic be haviors. In this paper， we present a coupled dynamic model with 16 degrees of freedom for the multi-body system of barge-type off shore floating wind turbines under the combined action of wind and waves. The model accuracy is verified through numerical simu lation using OpenFAST， developed by the National Renewable Energy Laboratory （NREL）. In particular， the modified Blade El ement Momentum theory is used to calculate the blade aerodynamic load， the linear potential flow theory is used to determine the wave load， and the quasi-static method is used to obtain the tension of the mooring systems. Besides the generator torque control and blade pitch control， a bi-directional tuned mass damper （TMD） is placed in the nacelle to mitigate the structural vibration of the floating wind turbine of the barge?type， where a limiting device is introduced to limit the TMD stroke. Subsequently， the con trol parameters are optimized by the method of exhaustion and the genetic algorithm. The simulation analyses show that the model proposed in this paper accurately alculates yields the dynamic response of the barge-type offshore floating wind turbine. The bi-di rectional TMD with collision mechanism is efficient in mitigating the structural response.