Massive preparation of high quality graphene is critical for the wide application of graphene.Recently,chemical vapor deposition (CVD) of carbon sources on transition metals surfaces is looked as a promising way,while the growth mechanism of graphene is not clear.Combined density functional (DFT) calculations,molecular dynamics (MD) simulations,thermodynamics analysis,and kinetic Monte Carlo (kMC) simulations,the possible nucleation processes,and the growth kinetics on Cu and Ir surfaces are investigated.