Homogeneous nucleation process in the vapor phase of water is investigated with a molecular dynamics computer simulation at 350 K under supersaturation ratio 7.3. Using a method similar to Lennard-Jones fluid (Part I), the nucleation rate is three orders of magnitude smaller than prediction of a classical nucleation theory. The kinetically defined critical nucleus size is 30-45, much larger than the thermodynamically defined value of 1.0 estimated with the classical theory. Free energy of cluster formation is estimated from the cluster size distribution in steady state time region. The predicted nucleation rate with this free energy agrees with the simulation result. It is concluded that considering the cluster size dependence of surface tension is very important.