Molecular dynamics computer simulation of a water system was carried out to investigate the dynamics of vapor phase homogeneous nucleation at 350 K under super saturation ratio 14.6. To control the system temperature, 5000 target particles were mixed with 5000 carrier gas particles. The observed nucleation rate is three orders of magnitude smaller than prediction of a classical nucleation theory. From the cluster size distribution in steady state region, the free energy of cluster formation is estimated, which diminishes the difference between the theoretical prediction and the simulational result concerning the nucleation rate.