We have studied the interaction between two neutral oxygen vacancies and the electronic structures of oxygen divacancy in the monoclinic phase of HfO2 by performing the first-principles calculations. It is found that the vacancy–vacancy interaction depends not only on the distance but also on the coordination of the removed oxygen atoms. The oxygen divacancy is formed energetically by the removal of two fourfold coordinated oxygen atoms (O4) with a distance of about 2.73 Å. The interaction between two O4 vacancies is attractive, indicating that the O4 vacancies tend to form stable cluster in HfO2. The oxygen divacancy induces two in-gap defect levels, which correspond to a bonding state and an anti-bonding one. These results would provide insightful information to understand the formation of conductive filaments in HfO2-based resistive random access memory devices.