A floating wind power platform for offshore power production, comprising: a floating unit, wherein the floating unit comprises a first, a second and a third interconnected semisubmersible column each being arranged in a respective corner of the floating unit, wherein a tension leg device is arranged to the third semisubmersible column, wherein the tension leg device is adapted to be anchored to the seabed by an anchoring device, and wherein the third semisubmersible column provides a buoyancy force adapted to create a tension force in the tension leg device, wherein the floating wind power platform is further adapted to weather vane in relation to the wind direction.