In this study, using first-principles calculations, we investigated the interfacial nature between single-walled carbon nanotubes (CNTs) and clean Al2O3(0001) surfaces. The calculation results showed that the adhesive energy of CNTs and clean Al2O3(0001) depends on the diameter of CNTs. The structures of the CNTs adsorbed on Al-terminated Al2O3(0001) do not drastically change from those before adsorbing. C atoms of CNTs interacted with the topmost Al atom of Al2O3(0001) by forming covalent bonding. In the case of the O-terminated Al2O3(0001), small-diameter CNTs have strong interaction, which comes from the opening of CNTs catalytically induced by the O-terminated surface and the subsequent formation of mixed covalent-ionic bonding between C and O atoms. This strong interfacial interaction also leads to significant charge transfer from the CNTs to the O-terminated Al2O3(0001). The strong interfacial interaction of small diameter CNTs with the O-terminated Al2O3(0001) would be a possible mechanism for the successful Al2O3 composite reinforced with CNTs.