Aiming at the problem that the existing analysis methods for the floating offshore wind turbine （FOWT） cannot efficiently predict the random dynamic response when considering the nonlinear coupling model，a fast calculation method of the random response of the FOWT nonlinear system under coupled wave excitation based on the statistical linearization algorithm is proposed，and its application in the vibration control of FOWT is studied. Taking the Spar FOWT as the object，a nonlinear model under the wave coupling excitation of 4-DOF is established based on the Lagrange equation，and the accuracy of the model is verified. On the basis of the established nonlinear model，a random vibration analysis method for this Spar FOWT based on statistical linearization algorithm is proposed，and the method is verified in many aspects. The results show that the method can improve the calculation efficiency by 4~5 orders of magnitude and has sufficient accuracy. The method is applied to the vibration control of the FOWT. The optimization of the control parameters and performance analysis of the FOWT under the control of TMD are efficiently realized，and the optimal control parameters of TMD are obtained. It is found that the vibration control effect of TMD on the FOWT tends to decrease gradually with an increase of the sea state level. In general，the proposed method has high accuracy，high efficiency and generality in different sea conditions，and also provides an efficient analysis method for the design optimization，fatigue analysis，reliability analysis and other research based on statistical characteristics of FOWT.