Localized surface plasmon resonance (LSPR) optical fiber biosensing is an advanced and powerful label-free technique which gets great attention for its high sensitivity to refractive index change in surroundings. However, the pursuit of a higher sensitivity is still challenging and should be further investigated. In this paper, based on a monolayer graphene/gold nanoparticles (Grm/Au NPs) three-dimensional (3D) hybrid structure, we fabricated a D-shaped plastic optical fiber (D-POF) LSPR sensor using a facile two-step method. The coupling enhancement of the resonance of this multilayer structure was extremely excited by the surface plasmon property of the stacked Au NPs/Grm layer. We found that the number of plasmonic structure layers was of high importance to the performance of the sensor. Moreover, the optimal electromagnetic field enhancement effect was found in three-layer plasmonic structure. Besides, the n*(Grm/Au NPs)/D-POF sensor exhibited outstanding performance in sensitivity (2160 nm/RIU), linearity (linear fitting coefficient R2 = 0.996) and reproducibility. Moreover, the sensor successfully detected the concentration of glucose, achieving a sensitivity of 1317.61 nm/RIU, which suggested a promising prospect for the application in medicine and biotechnology.