The problem of damaged tendon diagnosis (damage detection, damaged tendon identification and damage precise quantification) in a new multibody offshore platform supporting a 10 MW Floating Offshore Wind Turbine (FOWT) is investigated for the first time in this study. Successful operation of the multibody FOWT depends on the integrity of its tendons connecting the upper and lower tanks of the platform. Thus, early diagnosis of the damaged tendons is of high importance and it is achieved through a vibration-based methodology. Damage detection is accomplished based on the detection of changes in the vibration response power spectral density, while damaged tendon identification and damage precise quantification are accomplished through the Functional Model Based Method (FMBM). The FMBM is appropriately formulated in this study to operate with only vibration response signals. The employed vibration responses under healthy and damaged states of the FOWT platform are obtained from a numerical model describing the platform’s dynamics.