This paper presents switching linear parameter-varying (SLPV) control of a floating offshore wind turbine on a semisubmersible platform above rated wind speed for both power regulation and platform motion reduction. By linearizing a control-oriented nonlinear model at a series of operating points, a family of linear time-invariant models are obtained and directly used to design the SLPV controllers. FAST (Fatigue, Aerodynamics, Structures, and Turbulence) simulations using realistic wind profiles show that the SLPV controller outperforms a baseline controller, an H _∞ controller and a non-switching LPV controller in terms of power regulation and platform motion suppression.