The growth of graphene on oriented (111) copper films has been achieved by atmospheric pressure chemical vapor deposition. The structural properties of as-produced graphene have been investigated by scanning tunneling microscopy. Anomalous moiré superstructures composed of well-defined linear periodic modulations have been observed. We report here on comprehensive and detailed studies of these particular moiré patterns present in the graphene topography revealing that, in certain conditions, the growth can occur on the oxygen-induced reconstructed copper surface and not directly on the oriented (111) copper film as expected.