This paper describes the results of more than 4,000 long-term (up to thousands of peak-wave periods) numerical simulations of nonlinear gravity surface waves performed for investigation of properties and estimation of statistics of extreme («freak») waves. The method of solution of 2-D potential wave’s equa-tions based on conformal mapping is applied to the simulation of wave behavior assigned by different initial conditions, defined by JONSWAP and Pierson-Moskowitz spectra. It is shown that nonlinear wave evolution sometimes results in appearance of very big waves. There are no predictors for appearance of extreme waves, however, a height of dimensional waves is proportional to a significant wave height. The initial generation of extreme waves can occur simply as a result of group effects, but in some cases the largest wave suddenly starts to grow. It is followed sometimes by a strong concentration of wave energy around a peak vertical. It is taking place throughout several peak wave periods. It happens to an individual wave in a physical space, no energy exchange with surrounding waves taking place. Probability function for steep waves has been constructed. Such a function can be used for development of operational forecast of freak waves based on a standard forecast.