We developed a facile approach toward hybrid AgNP-graphene-AgNP sandwiched structures using self-organized monolayered AgNPs from wet chemical synthesis for the optimized enhancement of the Raman response of monolayer graphene. We demonstrate that the Raman scattering of graphene can be enhanced 530 fold in the hybrid structure. The Raman enhancement is sensitively dependent on the hybrid structure, incident angle, and excitation wavelength. A systematic simulation is performed, which well explains the enhancement mechanism. Our study indicates that the enhancement resulted from the plasmonic coupling between the AgNPs on the opposite sides of graphene. Our approach towards ideal substrates offers great potential to produce a "hot surface" for enhancing the Raman response of two-dimensional materials.