This paper describes a multilayer localized surface plasmon resonance (LSPR) graphene biosensor that includes a layer of graphene sheet on top of the gold layer, and the use of different coupled configuration of a laser beam. The study also investigates the enhancement of the sensitivity and detection accuracy of the biosensor through monitoring biomolecular interactions of biotin-streptavidin with the graphene layer on the gold thin film. Additionally, the role of thin films of gold, silver, copper and aluminum in the performance of the biosensor is separately investigated for monitoring the binding of streptavidin to the biotin groups. The performance of the LSPR graphene biosensor is theoretically and numerically assessed in terms of sensitivity, adsorption efficiency, and detection accuracy under varying conditions, including the thickness of biomolecule layer, number of graphene layers and operating wavelength. Enhanced sensitivity and improved adsorption efficiency are obtained for the LSPR graphene biosensor in comparison with its conventional counterpart; however, detection accuracy under the same resonance condition is reduced by 5.2% with a single graphene sheet. This reduction in detection accuracy (signal to noise ratio) can be compensated for by introducing an additional layer of silica doped B2O3 (sdB2O3) placed under the graphene layer. The role of prism configuration, prism angle and the interface medium (air and water) is also analyzed and it is found that the LSPR graphene biosensor has better sensitivity with triangular prism, higher prism angle, lower operating wavelength and larger number of graphene layers. The approach involves a plot of a reflectivity curve as a function of the incidence angle. The outcomes of this investigation highlight the ideal functioning condition corresponding to the best design parameters.