Graphene films grown by chemical vapour deposition have unusual physical and chemical properties that offer promise for applications such as flexible electronics and high-frequency transistors(1-10). However, wrinkles invariably form during growth because of the strong coupling to the substrate, and these limit the large-scale homogeneity of the film(1-4,11,12). Here we develop a proton-assisted method of chemical vapour deposition to grow ultra-flat graphene films that are wrinkle-free. Our method of proton penetration(13-17) and recombination to form hydrogen can also reduce the wrinkles formed during traditional chemical vapour deposition of graphene. Some of the wrinkles disappear entirely, owing to the decoupling of van der Waals interactions and possibly an increase in distance from the growth surface. The electronic band structure of the as-grown graphene films shows a V-shaped Dirac cone and a linear dispersion relation within the atomic plane or across an atomic step, confirming the decoupling from the substrate. The ultra-flat nature of the graphene films ensures that their surfaces are easy to clean after a wet transfer process. A robust quantum Hall effect appears even at room temperature in a device with a linewidth of 100 micrometres. Graphene films grown by proton-assisted chemical vapour deposition should largely retain their intrinsic performance, and our method should be easily generalizable to other nanomaterials for strain and doping engineering.