The complex dielectric functions and refractive index of atomic layer deposited HfO(2) were determined by the line scan method of the valence electron energy loss spectrum (VEELS) in a scanning transmission electron microscope (STEM). The complex dielectric functions and dielectric constant of monoclinic HfO(2) were calculated by the density functional theory (DFT) method. The resulting two dielectric functions were relatively well matched. On the other hand, the refractive index of HfO(2) was measured as 2.18 by VEELS analysis and 2.1 by DFT calculation. The electronic structure of HfO(2) was revealed by the comparison of the inter-band transition strength, obtained by STEM-VEELS, with the density of states (DOS) calculated by DFT calculation.