We have studied the dielectric properties of the cubic HfO2 thin film using first-principles ground-state calculations in external electric fields. We have evaluated the optical and the static dielectric constants for the cubic (c-) and the strained c-HfO2(001) films. The hydrogen termination of the surface suppresses the dielectric constant near the surface. The spatial variation of the local dielectric constant inside the film is very small. The static dielectric constant becomes larger with increasing lateral lattice constant and smaller if the constraint of the cubic symmetry is relaxed and two oxygen atoms in a unit cell becomes unequivalent. These results indicate that the change in dielectric constant can be attributed to the increase of the tetragonality in the film.