In this study, a numerical methodology based on the multiphase flow model was developed for predicting frost growth on a cooled surface. The proposed numerical methodology was validated by comparing the results of numerical simulations with measured data obtained from the present experiment. The slow-time acceleration technique was applied to reduce the computational time required for the simulation. The results demonstrated that the developed methodology accurately predicts the distribution of the ice phase volume fraction, the humid air streamline, temperature, and velocity magnitude. Furthermore, the slow-time acceleration technique significantly reduces the computational time required without sacrificing accuracy. Therefore, the developed methodology can be used to predict frost growth with good accuracy and reduced computational time, which has practical implications for various applications.