Formation energies and electronic properties of oxygen vacancies (Vo's) in amorphous HfO2 gate dielectrics are investigated by employing the first-principles method based on the density functional theory. We have found that the formation energy of neutral oxygen vacancy in amorphous HfO2 distributes from 4.7 to 6.1 eV, most of which is lower than the value for cubic HfO2, 6.0 eV. We also investigated the stabilities of the Vo pairs in various charged state and compared with those in amorphous SiO2. We found that the Vo++ is stabilized in the vicinity of the Vo in SiO2. In HfO2, however, this does not happen. This suggests the difference of defect propagation mechanism in HfO2 and SiO2.