Graphene growth at low temperatures (below 500 oC) on copper catalyst by CVD method was studied. The goal of this study is to determine a minimum growth temperature for growing graphene with high quality. In this study, the catalyst used for growing graphene was copper foil (Sigma-Aldrich, code: 1001328641, 25 µm in thickness, 99.98% trace metals basis, cut into 2x1 cm2 in size)  annealed at 900 oC , while the precursor used was poly(methyl methacrylate) (PMMA) heated at 140 oC. In graphene growth, two different growth temperatures of 350 oC and 450 oC were varied. The graphene films grown on copper foil catalyst were characterised using SEM and Raman spectroscopy. While, the films transferred onto quartz/glass/grid substrates were characterised by using SEM, Raman spectroscopy, UV-vis spectroscopy, four point probe and TEM. Results of this study showed that the 450 oC-grown samples produce a better quality graphene film compared to the 350 oC-grown samples. In other words, the minimum temperature of graphene growth is at least 450 oC for a Cu foil, since this temperature has to be sufficiently high to activate carbon diffusion and rearrangement on the catalyst surface..