The behavior of deep-water gravity waves under the effect of wind and viscosity is studied. It is analyzed, how random wind affects the Peregrine breather, which is considered as a possible prototype of extreme waves in the oceans. Using the Euler equations of fluid dynamics and the method of multiple scales, the nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation are obtained for the case of nonlinear deep water waves forced by random wind. For modeling the wind forcing of ocean waves, Miles’ theory is extended to include time varying random wind velocity processes, which leads to stochastic partial differential equations. For different regimes of stochastic wind it is shown that perturbed versions of the Peregrine solution occur also under strong gusty wind conditions and lead to extreme waves as well. Moreover, the improved modeling using the modified nonlinear Schrödinger equation does not considerably change this behavior.