We developed a new coarse-grained (CG) model for water to study nucleation of droplets from the vapor phase. The resulting potential has a more flexible functional form and a longer range cutoff compared to other CG potentials available for water. This allowed us to extend the range of applicability of coarse-grained techniques to nucleation phenomena. By improving the description of the interactions between water molecules in the gas phase, we obtained CG model that gives similar results than the all-atom (AA) TIP4P model but at a lower computational cost. In this work we present the validation of the potential and its application to the study of nucleation of water droplets from the supersaturated vapor phase via molecular-dynamics simulations. The computed nucleation rates at T = 320 K and 350 K at different supersaturations, ranging from 5 to 15, compare very well with AA TIP4P simulations and show the right dependence on the temperature compared with available experimental data. To help comparison with the experiments, we explored in detail the different ways to control the temperature and the effects on nucleation.