Interfacial atomic structures of Cu/Al₂O₃(0001) and Cu/Al₂O₃(112̅0) systems prepared by a pulsed-laser deposition technique have been characterized by using high-resolution transmission electron microscopy (HRTEM). It was found that Cu metals were epitaxially oriented to the surface of Al₂O₃ substrates, and the following orientation relationships (ORs) were found to be formed: (111)_Cu//(0001)Al₂O₃, [11̅0]_Cu//[11̅00]Al₂O₃ in the Cu/Al₂O₃(0001) interface and (001)_Cu//(112̅0)Al₂O₃, [11̅0]_Cu//[0001]Al₂O₃ in the Cu/Al₂O₃(112̅0) interface. Geometrical coherency of the Cu/Al₂O₃ system has been evaluated by the coincidence of reciprocal lattice points method, and the result showed that the most coherent ORs were (111)_Cu//(0001)Al₂O₃, [112̅]_Cu//[11̅00]Al₂O₃ and (11̅0)_Cu//(112̅0)Al₂O₃, [111]_Cu//[0001]Al₂O₃, which are equivalent to each other. These ORs were not consistent with the experimentally observed ORs, and it was possible that crucial factors to determine the ORs between Cu and Al₂O₃ were not only geometrical coherency, but also other factors such as chemical bonding states. Therefore, to understand the nature of the interface atomic structures, the electronic structures of the Cu/Al₂O₃ interfaces have been investigated by electron energy-loss spectroscopy. It was found that the pre-edge at the lower energy part of the main peak appeared in the O-K edge spectra at the interface region in both the Cu/Al₂O₃(0001) and Cu/Al₂O₃(112̅0) systems. This indicates the existence of Cu–O interactions at the interface. In fact, HRTEM simulation images based on O-terminated interface models agreed well with the experimental images, indicating that O-terminated interfaces were formed in both systems. Since the overlapped Cu atomic density in the experimental ORs were larger than that in the most coherent OR, it is considered that the on-top Cu–O bonds stabilize the O-terminated Cu/Al₂O₃ interfaces.