In this paper, based on lattice-Boltzmann method (LBM), the steam condensation and growth of a droplet on the horizontal cold wall and falling down on vertical wall has been simulated. The Lee’s LBM model which is stable in the high density and viscosity ratios is used. This method is accompanied with solving the temperature equation and adding a phase change source term. The Lee model is based on Cahn-Hilliard theory which is assumed to be incompressible flow and therefore the velocities of the flow are divergence-free. when phase change occurs this condition will not be satisfied. A phase change source term is added on the interface of gas and liquid phase. Solution of temperature field in a passive scalar method of solving the flow field is separated and Boussinesq assumption would be influence the flow field of the temperature field. The density ratio of 25 is considered to be in this paper which is density ratio of steam and water. The model is extended to two dimensions (D2Q9) to simulate droplet condensation. The simulation results are compared in various grids. The effects of gravitational acceleration, equilibrium contact angle, the cold wall and also the mass conservation, have been investigated separately. Finally the stream field for the different time step has been analyzed.