Rain droplet formation due to condensational growth and small-scale turbulent fluctuations is investigated. We report here the results of Monte Carlo type simulations of the droplet activation on cloud condensation nuclei and subsequent condensational growth in a turbulent cloud medium. According to modeling results relatively small fluctuations in temperature and water vapor concentration play essential role in droplet size distribution broadening and producing big cloud droplets, responsible for onset of fast coalescence growth and initiation of precipitation.