The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with free surface written in a surface-following non-orthogonal curvilinear coordinate system where depth is counted from moving surface. А three-dimensional Poisson equation for velocity potential is solved iteratively. А Fourier transform method, the second-order accuracy approximation of vertical derivatives on a stretched vertical grid and the fourth-order Runge–Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of the earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of wave field with thousands degrees of freedom over thousands of wave periods. A long-time evolution of two-dimensional wave structure is illustrated by the spectra of wave surface and input and output of energy.