Graphene has attracted a lot of interest due to its intriguing electronic and mechanical properties,which strongly depend on its thickness.It is important to understand the graphene-metal interaction to control its thickness during its growth on metal surfaces.Here,we used the DFT-D2 method of Grimme,which includes the critical long-range van der Waals forces in the graphene-metal interaction,to study the interfaces between mono-,bi-,and trilayer graphene and Cu and Ni(111)surfaces.Our results show the adsorption energy increases with the increase of graphene layers on Ni(111); in contrast,it decreases on Cu(111).Charge density and partial density of states analyses show that monolayer graphene adsorbed on Ni(111)is more reactive than that on Cu(111).Another graphene layer can be easily formed on top of monolayer or bilayer graphene adsorbed on Ni(111); but not on Cu(111).These findings provide a useful guide for achieving precise layer controlled graphene growth and designing graphene based devices.