Numerical study on the condensed and frozen vapor on a flat plate was performed to estimate the trends of the freezing of water vapor and its thickness. For the simulation of the phase change of water vapor for the freezing, VOF(Volume of Fluid) method was used. As the freezing area growth, we investigated the flow-velocity variation in the wall-normal direction. Zero-velocity region in the frozen layer was calculated using the Carman-Kozeny equation deriving from the Darcy law in the momentum equation. The phase change rate was assumed to be mainly related the temperature difference between a plate and atmosphere. Basic concept of the freezing phenomenon was combined with the condensation vapor schematics. The calculation for the volumetric generation rate and the freezing rate of water-vapor was controlled by the thermophysical approaches and the enthalpy-porosity method to model the condensation and the freezing, respectively. The numerical simulation was conducted using an open source code, named OpenFOAM®. The obtained results were compared to the corresponding references for the variation of the frozen thickness by the phase change. The comparison of the prediction results with the reference data showed god agreement. Also, positive possibilities of the performance for obtaining better results are expected by using additional complements in further studies.