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This paper investigates the enhancement of sensitivity of variable incidence angle LSPR biosensor by monitoring biomolecular interactions of biotin-streptavidin with gold thin film. The investigation is carried out by means of introducing an additional layer of graphene sheet on top of gold layer (graphene biosensor) and using different coupling configuration of laser beam. The sensitivity, which is indicated by the shift of plasmon resonance angle, increases with graphene deposited onto the gold layers and is linearly related with the number of graphene layers. In addition, an investigation of the shift of plasmon dip is carried out for two different analyte interfaces: air and water. It is found that graphene biosensor has better sensitivity for triangular prism, higher prism angle, and water interface. The evaluation approach involves a plot of a reflectivity curve as a function of the angle of incidence while the operating wavelength is kept fixed.