Usually, for the estimation of the cloud droplet size in the equilibrium state, Kohler equation is utilized, assuming constant vapor pressure and constant temperature. However, consumption of the ambient vapor due to condensational growth decreases the ambient water vapor pressure and increases the temperature. Taking account of the variations of the water vapor content and the temperature, a new model for the estimation of the equilibrium cloud droplet size, saturation ratio and temperature has been developed with use of the mass and the heat conservation laws. These laws are applied for the control volume of the air parcel which contains multi-sized CCN. Variations of droplet size, decrement of saturation ratio and increment of temperature with CCN composition (size and number) in air parcel are simulated numerically. The results of numerical simulations with this model show that competitive growth of droplets on multi-sized CCN is controlled by large size CCN.