The dielectric constant of water confined in a nanodimensional spherical cavity is calculated by means of molecular dynamics simulations. The simulations are carried out by using two different water models: soft sticky dipole and simple point charge/extended. Three different sizes of the confining cavity are considered for each water model. For both the models, the dielectric constant of water in the cavity is found to be significantly smaller than that of bulk water. A nearly 50% decrease of the dielectric constant is observed when water is confined in a cavity of about 12 Angstrom in diameter. In the present models, there is no electrostatic interaction between water and the cavity surface, and thus, the reduction of the dielectric constant observed in this study is purely a result of confinement.