Wrinkles are ubiquitous for graphene films grown on various substrates by chemical vapor deposition at high temperature due to the strain induced by thermal mismatch between the graphene and substrates, which greatly degrades the extraordinary properties of graphene. Here we show that the wrinkle formation of graphene grown on Cu substrates is strongly dependent on the crystallographic orientations. Wrinkle-free single-crystal graphene was grown on a wafer-scale twin-boundary-free single-crystal Cu(111) thin film fabricated on sapphire substrate through strain engineering. The wrinkle-free feature of graphene originated from the relatively small thermal expansion of the Cu(111) thin film substrate and the relatively strong interfacial coupling between Cu(111) and graphene, based on the strain analyses as well as molecular dynamics simulations. Moreover, we demonstrated the transfer of an ultraflat graphene film onto target substrates from the reusable single-crystal Cu(111)/sapphire growth substrate. The wrinkle-free graphene shows enhanced electrical mobility compared to graphene with wrinkles.