We report the fabrication of graphene-encapsulated nanoballs with copper nanoparticle (Cu NP) cores whose size range from 40 nm to 1 μm using a solid carbon source of poly(methyl methacrylate) (PMMA). The Cu NPs were prone to agglomerate during the annealing process at high temperatures of 800 to 900 °C when gas carbon source such as methane was used for the growth of graphene. On the contrary, the morphologies of the Cu NPs were unchanged during the growth of graphene at the same temperature range when PMMA coating was used. The solid source of PMMA was first converted to amorphous carbon layers through a pyrolysis process at the temperature regime of 400 °C, which prevented the Cu NPs from agglomeration, and they were converted to few-layered graphene (FLG) at the elevated temperatures. Raman and transmission electron microscope analyses confirmed the synthesis of FLG with thickness of approximately 3 nm directly on the surface of the Cu NPs. X-ray diffraction and X-ray photoelectron spectroscopy analyses, along with electrical resistance measurement according to temperature changes showed that the FLG-encapsulated Cu NPs were highly resistant to oxidation even after exposure to severe oxidation conditions.