Abstract: An improved method based on S-N curve and fracture mechanics is proposed to evaluate the fatigue life of tethers of tension leg type floating offshore wind turbine（FOWT）under combined action of wind,current and wave. Firstly,the stress time history of tethers is obtained by time-domain coupling analysis. Then,the fatigue life at crack initiation stage is evaluated based on S-N curve of crack initiation and linear cumulative damage theory,while the fatigue life at the non-through crack propagation stage and through crack propagation stage was evaluated based on Forman formula of fracture mechanics. Finally,the feasibility of the method is verified by taking a 5 MW Seastars floating wind turbine as an example,and the effects of pre-tension and angles of wind,current and wave on fatigue life were studied. The results show that the fatigue life at through crack propagation stage accounted for extremely small proportion of the total fatigue life;Fatigue life decreases with the increase of the pre-tension,and is sensitive to the change of the angle of wind,current and wave.