We report the synthesis of Cu2O single crystalline films on the c-plane alpha-Al2O3 substrate by radio-frequency plasma assisted molecular beam epitaxy. An ultrathin MgO layer was adopted to modify the complex surface structure of sapphire (0001) and engineer the interfacial atomic matching between the epilayer and the substrate. The experimental results solidly proved the single crystallinity of cubic Cu2O (111) without twin crystals. A coincident match mode was proposed to explain the unusual in-plane orientation between strained MgO (111) and Cu2O (111). It was found that the crystal quality of Cu2O is very sensitive to the thickness of MgO layer, which is optimized to be similar to 2 nm. The reason why MgO has a critical thickness in Cu2O single crystal growth was also tentatively discussed. (C) 2012 Elsevier B.V. All rights reserved.