The HfO2 thin-film growth process is investigated by using in situ real-time spectroscopic ellipsometry (SE) technique combined with the first-principles molecular-orbital (MO) calculations of the electronic states. The HfO2 films are grown on the silicon substrate by using the pulsed-source metal-organic chemical-vapor deposition method. Particular attention is paid to the formation of an interfacial layer at the early stage of the growth process by monitoring energy-dependent dielectric constants of the film. The energy dependence of the electronic polarizabilities and dielectric constants is calculated for the amorphous HfO2, SiO2, and HfSiO4 films based on the electronic states and density of states obtained using the discrete-variational Xα MO method with the unit cluster model. The measured SE spectra show that the average dielectric constants of the film vary gradually from those for SiO2 to those for HfO2 when the number of deposition cycles increases. By comparing the varied dielectric constants during the film growth with the calculated results, we find that the HfO2 film growth process can be divided into two stages with different growth mechanisms: SiO2 and HfxSiyOz layers are grown at the first stage, which are regarded as the interfacial layers, and the HfO- 2 layer formation becomes predominant at the second stage.