A kinetic model of the solar wind based on Kappa velocity distribution functions for the electrons and protons escaping out of the corona is presented. The high velocity particles forming the tail of these distribution functions have an enhanced phase space density compared to a Maxwellian. The existence of such velocity distribution functions have been introduced in the pioneering work of Scudder (1992a,b) to explain the high temperature of the coronal plasma. The first results obtained with this new kinetic model of the solar wind are very encouraging, indeed they fit better many major features observed in the solar wind than earlier models: e.g. the large bulk velocities observed in high speed streams emitted out of coronal regions where the plasma temperature is smaller, and the low speed solar wind originating in the hotter equatorial regions of the solar corona. This new kinetic model is also able to predict the high speed solar wind streams without unreasonably large coronal temperatures and without additional heating of the outer region of the corona, as it is needed in hydrodynamic models to achieve the same solar wind speed.