The emission characteristics of fluorescent molecules near the surface of noble metals have changed significantly due to the influence of surface plasmon resonance (SPR). They are widely used in the design of nano-devices such as fluorescent probes. The energy transfer mechanism between fluorescent molecules and metals is the basis for the design of such fluorescent probes. Therefore, in this paper, surface energy transfer (SET) and metal regulated spontaneous emission effect of single fluorescent molecules in the Au/SiO₂/Ag core-shell nanostructure were theoretically simulated by using finite difference time domain (FDTD) method. The SET between fluorescent molecules and the hybrid plasmonic mode was studied. The results showed that due to the local surface plasmon resonance coupling between gold core and silver shell, the energy transfer efficiency between fluorescent molecules and metals shows a d¹⁰ relationship, which d is the distance from the fluorescent molecules to gold surface. That result is obviously different from the conventional FRET effect and the SET effect of single metal structure. It is expected to be applied in the development of nano light sources and biosensors.