For the three kinds of composite materials, i.e., Cu(111)/HfO2(001), Cu(111)/HfO2(010) and Cu(111)/HfO2(100), the first-principles method based on the density functional theory is adopted to calculate their rates of mismatching of interface model, interface adhesion energies, the electric charge densities, the electron localization functions, and the charge density differences separately. The results indicate that the rate of mismatching of the Cu(111)/HfO2(010) interface model is lowest and its interface adhesion energy is higher than the others’, which means that the Cu(111)/HfO2(010) is most stable. From the analyses of charge densities and electron localization functions of the three interfaces, it can be found that only the Cu(111)/HfO2(010) interface is able to form the connective electronic channel along the vertical direction of the Cu electrode. This indicates that electrons possess the localizabilty and connectivity along the HfO2(010) direction, which corresponds to the switching-on direction of the resistive random access memory (RRAM) device. The charge density difference analysis reveals that the charge density distributions overlap, the electrons transfer mutually and bond at the interface of the Cu(111)/HfO2(010). In addition, based on the model of Cu (111)/HfO2 (010) interface, the formation energies of the interstitial Cu at different positions are also calculated. The results show that the closer to the interface the Cu atom, the more easily it migrates into HfO2. This indicates that the electrochemical reaction takes place more easily under the applied voltage, which results in the formation and rupture of Cu conductive filaments. All the above findings will provide a theoretical guidance for improving the performances of RRAM devices.