A D-shape plastic optical fiber (D-POF) surface plasmon resonance (SPR) biosensor based on the graphene/Au film (G/Au) was proposed and experimentally demonstrated for detection of DNA hybridization process. To improve the detection performance of SPR sensors, the Physical Vapor Deposition (PVD) method was used to evaporate the Au film directly onto the graphene grown on copper foil, and the Au film acted as a role of traditional Polymethyl Methacrylate (PMMA). The process made graphene and Au film form seamless contact. Next, the G/Au was transferred onto the D-shape fiber together. We explored the G/Au SPR sensor by using the finite element method (FEM) and obtained the optimum materials thickness to form configuration. Compared to other plastic optical fiber experiments, the proposed sensor's sensitivity was improved effectively and calculated as 1227 nm/RIU in a range of glucose solution. Meanwhile, our proposed sensor successfully distinguishes hybridization and single nucleotide polymorphisms (SNP) by observing the resonance wavelength change. It also exhibits a satisfactory linear response (R2 = 0.996) to the target DNA liquids with respective concentrations of 0.1nM to1µM, which shows this method's wide potential in medical diagnostics.