We performed molecular dynamics simulations of the nucleation of water vapor in order to test nucleation theories. Simulations were performed for a wide range of supersaturation ratios (S = 3-25) and water temperatures (T w = 300-390 K). We obtained the nucleation rates and the formation free energies of a subcritical cluster from the cluster size distribution. The classical nucleation theory and the modified classical nucleation theory (MCNT) overestimate the nucleation rates in all cases. The semi-phenomenological model, which corrects the MCNT prediction using the second virial coefficient of a vapor, reproduces the formation free energy of a cluster with the size ≲20 to within 10% and the nucleation rate and cluster size distributions to within one order of magnitude. The sticking probability of the vapor molecules to the clusters was also determined from the growth rates of the clusters. The sticking probability rapidly increases with the supersaturation ratio S, which is similar to the Lennard-Jones system.