Abstract We have performed multiscale simulations of the growth of graphene on defect-free copper (111) in order to model the nucleation and growth of graphene flakes during chemical vapour deposition and potentially guide future experimental work. Basic activation energies for atomic surface diffusion were determined by ab initio calculations. Larger scale growth was obtained within a kinetic Monte Carlo approach (KMC) with parameters based on the ab initio results. The KMC approach counts the first and second neighbours to determine the probability of surface diffusion. We report qualitative results on the size and shape of the graphene islands as a function of deposition flux. The dominance of graphene zigzag edges for low deposition flux, also observed experimentally, is explained by its larger dynamical stability that the present model fully reproduced.