Floating offshore wind turbines (FOWTs) are slender structures that are sensitive to hazardous conditions, mainly to winds. Wind action can cause undesirable vibrations that may affect safety and operability. These vibrations can be controlled in numerous ways through passive, active, semiactive or hybrid control. An example of passive control is a tuned mass damper (TMD) that dissipates mechanical energy from the main system when well-tuned to the structure. An inverted pendulum is a device that can be used as a TMD that vibrates out of phase in relation to the main system, reducing the vibrations in comparison to a classical TMD. This work describes a procedure for controlling a FOWT, which is subjected to wind actions, using a proposed tuned mass damper by means of an inverted pendulum (TMD-IP). TMD-IP is evaluated by two specific metrics: tower peak rotation and tower variance rotation. Optimization of the parameters of the inverted pendulum achieved reductions of approximately 95% for the rotation of the tower and the translation of the barge when a harmonic excitation is applied. Using the Monte Carlo method, random wind loading is applied to the FOWT; the reduction in the tower rotation is approximately 70%, and the reduction in the barge translation is approximately 80%. In addition, it is verified that changes in blade stiffness and damping alter the response of the structure very little when the FOWT is under extreme wind conditions. Finally, the results obtained through time and frequency domain analysis are closer to those. [ABSTRACT FROM AUTHOR]