With the rapid development of offshore wind power in recent years，the floating offshore wind turbine is proposed to capture more abundant and lasting wind energy in the deep sea，which has become the main direction of wind energy development. Due to the special structures and complex environment，the accurate calculation and analysis of floating offshore wind turbines will be particularly important for a multi-body system. In this paper，the coupling dynamic model of a floating offshore wind turbine is deeply studied. The improved 14-DOF coupling dynamic model of spar floating offshore wind turbine under complex working conditions is established，including an aerodynamic model，hydrodynamic model and structural analysis model，which can accurately calculate its dynamic response and verified by numerical simulation. The main improvements are as follows： expanding its scope of application without using small approximation of the angle in the coordinate rotation matrix； considering the conversion relationship between angular velocity and Euler angular velocity，the motion equation of floating offshore wind turbine with wider application range and more accuracy is derived. Besides，considering the influence of fan blade torsion angle on blade deformation，the accurate in-plane and out-of-plane response of the blade is obtained. Meanwhile，the potential flow theory is used to calculate the hydrodynamic force in order to solve the limitations of the traditional Morison equation algorithm. The simulation analysis shows that the model proposed in this paper can calculate the dynamic response of floating offshore wind turbine system more accurately with wider applicability.