Chemical vapour deposition of carbon-containing precursors on metal substrates is currently the most promising route for the scalable synthesis of large-area, high-quality graphene films 1 . However, there are usually some imperfections present in the resulting films: grain boundaries, regions with additional layers (adlayers), and wrinkles or folds, all of which can degrade the performance of graphene in various applications 2 , 3 , 4 , 5 , 6 , 7 . There have been numerous studies on ways to eliminate grain boundaries 8 , 9 and adlayers 10 , 11 , 12 , but graphene folds have been less investigated. Here we explore the wrinkling/folding process for graphene films grown from an ethylene precursor on single-crystal Cu–Ni(111) foils. We identify a critical growth temperature (1,030 kelvin) above which folds will naturally form during the subsequent cooling process. Specifically, the compressive stress that builds up owing to thermal contraction during cooling is released by the abrupt onset of step bunching in the foil at about 1,030 kelvin, triggering the formation of graphene folds perpendicular to the step edge direction. By restricting the initial growth temperature to between 1,000 kelvin and 1,030 kelvin, we can produce large areas of single-crystal monolayer graphene films that are high-quality and fold-free. The resulting films show highly uniform transport properties: field-effect transistors prepared from these films exhibit average room-temperature carrier mobilities of around (7.0 ± 1.0) × 10 3 centimetres squared per volt per second for both holes and electrons. The process is also scalable, permitting simultaneous growth of graphene of the same quality on multiple foils stacked in parallel. After electrochemical transfer of the graphene films from the foils, the foils themselves can be reused essentially indefinitely for further graphene growth.