Plasmon resonance plays an important role in improving the detection of biomolecules, and it is one of the focuses of research to use metal plasmon resonance to achieve fluorescence enhancement and to improve detection sensitivity. However, the problems of nondynamic tuning and fluorescence quenching of metal plasmon resonance need to be solved. Graphene surface plasmon resonance can be dynamically controlled, and the graphene adsorption of fluorescent molecules can avoid fluorescence quenching and greatly improve the fluorescence emission intensity. The graphene-metal hybrid structure designed in this work can solve the above two problems well, and the plasmon resonance can improve the fluorescence emission efficiency of molecules on the surface of graphene and improve the sensitivity of biological detection. At the same time, graphene nanoribbons in our hybrid structure do not require patterning, which greatly lowers the threshold for graphene application in biosensing.