n this paper we attempt to present a multilayered structure biosensor. A graphene-based surface plasmon resonance (SPR) biosensor is considered as a structure which offers the enhancement of sensitivity in comparison with the conventional biosensors. The sensitivity improvement caused by the presence of graphene is discussed through monitoring of the biomolecular interactions and following that the refractive index (RI) changes. For this purpose, a RI change which is increased during the course of biomolecular interactions is considered from 1.462 to 1.52. Our numerical results show that the proposed SPR biosensor with a graphene layer can provide a better sensitivity due to the field distribution at the binding region. This paper investigates the sensitivity enhancement factor (SEF) according to the S-parameters and the effects of design parameters such as the thicknesses of gold and graphene layers and the refractive index change during the course of DNA hybridization in this biosensor.