A new coarse-grained (CG) model is developed for water. Each CG unit consists of three charged sites, and there is an additional nonelectrostatic soft interaction between central sites on different units. The interactions are chosen to mimic the properties of 4-water clusters in atomistic simulations: the nonelectrostatic component is modeled using a modified Born-Mayer-Huggins potential, and the charges are chosen to reproduce the dipole moment and quadrupole moment tensor of 4-water clusters from atomistic simulations. The parameters are optimized to reproduce experimental data for the compressibility, density, and permittivity of bulk water and the surface tension and interface potential for the air-water interface. This big multipole water (BMW) model represents a qualitative improvement over existing CG water models; for example, it reproduces the dipole potential in membrane-water interface when compared to experiment, with modest additional computational cost as compared to the popular MARTINI CG model.