We present a nonlinear relationship between ocean surface wind at 10 m height (U,,) and significant wave height of wind-generated gravity waves, (H,,,)gw, over the open oceans using SEASAT radar altimeter data. The data represent a variety of fetches, durations and strength of winds. Concurrent measurement of significant wave height, (H,,& which may contain a measure of swell and U,, obtained from the processed geophysical data record (GDR) of the SEASAT radar altimeter were used in the analysis. The total wave energy, &, characterised by altimeter H,,3 measurements was compared with the energy of a fully developed sea, E',, derived from U,, measurements using the Pierson-Moskowitz model. The criteria ,!&, I E,,, was used in data selection to minimise the influence of swell. (H,,,)gw thus obtained was used in a regression in terms of U,, in a second-degree polynomial. Verification with independent radar altimeter data confirmed the validity of the proposed wind-wave model, which could be used for operational wave forecasting.