The capacity of wind turbines on offshore wind platforms is presently much greater than that for wave energy conversion. However, wind availability with speed greater than 5 m/s, just above cut in, is typically 30–40% requiring storage to provide uniformity of supply, but this may be improved by adding swell wave energy conversion with typical availability of 90%. A hybrid platform is considered with three effectively rigid cylindrical floats connected by beams at right angles to support a wind turbine with its base on the central float, and two wave energy floats, opposite the wind floats, with beams at 90° and hinges with dampers for mechanical energy absorption on the central float. With swell periods over 10 s, pitch resonance may be achieved with the fore and aft floats about half a wavelength apart with anti-phase forcing causing a moment on hinges above water level. The NREL 5 MW wind turbine is incorporated and average swell wave power absorption in a typical significant wave height of 2 m is over 200 kW. The analysis is by time domain linear diffraction–radiation modelling validated for other multi-float configurations. Significant wave energy conversion is omnidirectional over a wide range of heading angles. An added benefit is that in larger waves associated with strong winds, when the wave energy conversion would be disengaged, the wave float rotation on free hinges reduces the hub accelerations below that for rigid floats, enabling a longer time for wind power generation.