We demonstrate a mechanism of efficiently transforming surface plasmon polaritons (SPPs) into Cherenkov terahertz (THz) radiation. In a structure where multilayer graphene is deposited on a dielectric substrate with a buffer layer, the energy of the SPPs can be significantly enhanced. The dispersion of SPPs crosses the light line of the substrate if the buffer layer has a low permittivity relative to the substrate. As a result, the SPPs can be readily transformed into radiation without the need of wavevector compensation. Compared to the radiation from structures without graphene, the radiation power density is enhanced by nearly three orders of magnitude due to the field enhancement of SPPs. Our results could provide a promising way for developing room temperature, tunable, coherent, and intense THz radiation sources to cover the entire THz regime.