A highly sensitive Au-graphene structure D-type fiber surface plasmon resonance biosensor is presented in this study to specifically detect biomolecules. The method of growing graphene is employed directly on the copper, and then a gold film of optimum thickness is sputtered, and the copper foil is etched to obtain the structure. This method makes the contact closer between the gold layer and the graphene layer to improve surface plasmon resonance performance. The performance of this type of surface plasmon resonance (SPR) sensor has been previously verified both theoretically and experimentally. With the proposed Au-graphene structure D-type fiber biosensor, the SPR behaviors are obtained and discussed. In the detection of ethanol solution, a red shift of 40 nm is found between the refractive index of 1.3330 and 1.3657. By calculation, the sensitivity of the sensor we designed is 1223 nm/RIU. Besides, the proposed sensor can detect the nucleotide bonding between the double-stranded DNA helix structures. Thus, our sensors can distinguish between mismatched DNA sequences.