Motivated by the exciting potential of the new floating offshore wind concepts, this thesis aims to analyze the fatigue behavior of a novel semi-submersible floating offshore wind turbine, developed at CeSOS, NTNU, which consists of four cylindrical columns with one central column supporting the 5 MW NREL wind turbine. The geometry was proposed by the author, based on logic, mathematical derivations, as well as information from the literature. The SESAM package provided by DNV was used for this thesis, including GeniE, Sestra, Submod, SESAM Manager and Xtract. The geometry was developed in the FEM software GeniE, which uses Sestra as solver, while the rest of the tools were utilized for the sub-modeling technique. Two different geometries of the column-pontoon connection were designed and their performances under different loads were analyzed and compared. The model which appeared to be more reliable regarding fatigue was further investigated and optimized in order to reduce the SCF, which are of great importance for fatigue predictions. One crucial hot spot underwent a detailed stress analysis, using the sub-modeling technique, i.e. cutting the structure at a specified location and refining the mesh. The stress assessment at the location of interest was performed in Xtract, and for further extrapolation of the stress results in order to compute the hot spot stresses and the SCFs, an Excel spreadsheet was used. Using the load time series from the dynamic analysis of the global model, and combining them with the hot spot stresses, the stress time series were output for a certain sea state. The actual fatigue calculations were performed in Matlab, using the freely available WAFO package. First, the well-established uni-axial fatigue case was performed, utilizing the rainflow counting method, a proper S-N curve and the Miner's rule. A number of 13 sea states with 10 seeds each, with aligned wind and wave were considered. The fatigue assessment was performed for four different sea headings with respect to the pontoon's direction, i.e. 0, 30, 60 and 90 degrees. Next, an approach for considering multi-axial effects in fatigue analysis was proposed, combining two recently developed methods, Equilibrium Equivalent Structural Stress and the Path-Dependent Maximum Range. Considerations on the importance of multi-axial effects on the analyzed structure were further made, followed by conclusions and recommendations for future work.