We report the synthesis of large-scale uniform graphene films on high carbon solubility substrates of Rh foils for the first time using an ambient-pressure chemical vapor deposition method. We find that, by increasing the cooling rate in the growth process, the thickness of graphene can be tuned from multilayer to monolayer, resulting from the different segregation amount of carbon atoms from bulk to surface. The growth feature was characterized with scanning electron microscopy, Raman spectra, transmission electron microscopy, and scanning tunneling microscopy. We also find that bilayer or few-layer graphene prefers to stack deviating from the Bernal stacking geometry, with the formation of versatile moiré patterns. On the basis of these results, we put forward a segregation growth mechanism for graphene growth on Rh foils. Of particular importance, we propose that this randomly stacked few-layer graphene can be a model system for exploring some fantastic physical properties such as van Hove singularities.