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We used the APCVD growth system to carry out the segregation growth of graphene by using Rh as substrates. By controlling the growth conditions and the cooling rate after growth, we can controllably obtain monolayer graphene, bilayer graphene and multilayer graphene on Rh foils. Wrinkles can be observed on graphene synthesized on Rh foils, which is due to the mismatch of coefficient of thermal expansion between graphene and Rh substrates. The height of wrinkles on monolayer graphene and multilayer graphene is ~3 and ~10 nm, respectively, and the wrinkles have specific orientations, which are closely related to the lattice orientation of the Rh facets. We can also controllable synthesize bilayer graphene on Rh(111) substrate. However, there is no wrinkles observed, which is indicated that graphene wrinkles are originated on Rh grain boundaries and they are the main channel of stress release during the cooling process. Based on the growth characteristics of graphene, We propose the combined CVD and segregated growth mechanism of graphene on Rh substrates. The main path of carbon segregation is Rh grain boundaries, meanwhile the Rh atom steps and terraces are also the way for carbon segregation.