The composite substrate of Co and Cu was proposed to grow homogenous high quality wafer-size graphene films by an atmosphere pressure CVD method. The composite substrate consists of a moderate-carbon-solubility metal top (Co coating) as a C-dissolving layer and a low-carbon-solubility metal base (Cu foil) as a C-rejecting layer. During the CVD process, the interdiffusion of Co and Cu atoms occurs in the composite. With the dynamic control on Co and Cu alloying process to affect the carbon solubility, active carbon atoms captured by the Co layer were segregated to form spontaneously a high-quality graphene film on the top of Cu-Co substrate. The tunable layer-number of the graphene films can be precisely controlled by adjusting the thickness of the Co layer. High quality single-layered graphene films with a 98% yield were prepared on an 80 nm-Co-coated Cu foil and insensitive to growth temperature and time. More importantly, this type of composite substrate has also been developed to grow AB-stacked bilayers and three-layer graphene with 99% surface coverage and absence of defects. The approach is opening up a new avenue for high-quality graphene production with precise layer control through composite substrate design.