In this paper, a dynamic model for the offshore wind turbine installation is proposed. And this model is coupled by the wind turbine and the floating crane considering 6-DOF floating crane, 5-DOF wind turbine and elastic stretch of the hoisting cable. And when the wind turbine lands on the supporting structure, the displacement constraint is applied at the wind turbine. During the process, the relaxation of the hoisting cable is considered. In addition, the nonlinear hydrostatic force, environmental force, hoisting cable force and mooring force are considered as the external force. The motions of wind turbine and the floating crane are studied. From the numerical analysis, it is found that the release velocity, the release height and wave condition have a great effect on the motion of wind turbine.