Monolayer graphene is commonly grown on Cu substrates due to the self-limiting nature of graphene synthesis by chemical vapor deposition (CVD). Consequently, the growth of multilayer graphene by CVD has proven to be relatively difficult. This study demonstrates that the number of layers in graphene synthesized on a copper substrate can be precisely set by controlling the partial pressure of hydrogen gas used in the CVD process. This study also shows that a pressure threshold exists for a distinct transition from monolayer to multilayer graphene growth. This threshold is shown to be the boundary where the graphene growth process on Cu by CVD is no longer a self-limiting process. In addition, the multilayer graphene synthesized through the pressure control method forms in the Volmer-Weber mode with an AB stacking structure.