Light-matter interactions in two dimensional (2D) materials have given new momentum to nano optoelectronics since the observation of localized surface plasmons interacting with the excitons. Graphene, a typical metallic 2D crystal with high optical absorbance, can provide surface plasmon effects to proximate molecules as nanostructured metals do. The spontaneous emission rate can be enhanced by the coupling of plasmonic modes with the emission frequencies of organic molecules. However, most experimental and theoretical studies report graphene plasmonics in the terahertz to mid-infrared range. Here, we demonstrate the optical transition and significant amplification of singlet emission from phosphoric molecule on a graphene substrate, with simultaneous enhancement of triplet emission in the visible regime. The spectroscopic investigations ascribe these phenomena to the coupling of graphene plasmonic modes with molecular transient dipole. The modulation of emission channel and quantum efficiency is achieved by specifically controlling the organic molecular surface density on graphene. The single layer graphene is the most efficient substrate for plasmon coupling, however, remarkable strong PL intensity is achieved by forming multi-stacks of the organic molecule-graphene hybrid layer. This work suggests a novel route for the manipulation of organic molecular emissions using graphene plasmonics, and can be applied in developing photonic devices with high quantum efficiency.