The paper presents results related to graphene growth by the method of precipitation on the boundary between a transition metal (nickel or cobalt) and a dielectric (SiO2 ). The source of graphene is a thin evaporated carbon layer. Carbon in the annealing process diffunds through the transition metal and precipitates on the surface of the dielectric substrate as the structure cools down. Relatively thick layer of copper, which is evaporated over carbon as a cover, prevents carbon to diffund to the surface of the metallization. The structure of the metallization for graphene forming is then Cu/C/(transition metal)/SiO2 /Si. We consider the utilization of the diffusion barrier to be the contribution of our work to graphene formation using this method. Even though both transition metals are of similar features, the necessary conditions for growth of high- quality graphene are different. In case of nickel, long annealing times within the whole range of annealing temperatures are necessary, while in case of structures with cobalt annealing time of 20 minutes at 900°C is enough for graphene growth. By annealing the Cu(300 nm)/C(20 nm)/Ni(50 nm)/SiO2 structure at the temperature of 800 °C for 60 minutes we obtained single-layer graphene (SLG).