We demonstrate the growth of continuous monolayer graphene films with millimeter-sized domains on Cu foils under intrinsically safe, atmospheric pressure growth conditions, suitable for application in roll-to-roll reactors. Previous attempts to grow large domains in graphene have been limited to isolated graphene single crystals rather than as part of an industrially useable continuous film. With both appropriate pre-treatment of the Cu and optimization of the CH4 supply, we show that it is possible to grow continuous films of monolayer graphene with millimeter scale domains within 80 min by chemical vapour deposition. The films are grown under industrially safe conditions, i.e., the flammable gases (H2 and CH4) are diluted to well below their lower explosive limit. The high quality, spatial uniformity, and low density of domain boundaries are demonstrated by charge carrier mobility measurements, scanning electron microscope, electron diffraction study, and Raman mapping. The hole mobility reaches as high as ~5,7002 m(2) V(-1) s(-1) in ambient conditions. The growth process of such high-quality graphene with a low H2 concentration and short growth times widens the possibility of industrial mass production.