Water nucleation on an aerosol particle under conditions of fluctuating saturation ratio has been simulated in the present study. We have constructed a model which allows one to reduce the description of the problem to two parameters, namely, standard deviation of the saturation ratio and correlation time for the saturation ratio near an aerosol particle. In contrast to the former parameter, the importance of the latter one is not so evident, and we emphasize it here. The saturation ratio fluctuations enhance the nucleation probability on insoluble aerosol particles, this might be important for atmospheric and technical applications.