In this paper, we have presented a design and simulation of a graphene-coated surface plasmon resonance (SPR) based biosensor for targeting specific biological components. We have explicitly shown the detection of the hemoglobin level in blood samples and the glucose concentration level in urine samples by using the finite element method (FEM) based numerical simulation. In the blood component, the 0.001 refractive index increment causes a 6.1025 g/l hemoglobin (HB) level increment, which has been detected using this SPR based sensor with 200 deg/RIU angular sensitivity. Moreover, we have also detected the presence or absence of diabetes using the glucose concentration level in urine samples with this SPR sensor. Therefore, the novelty of this paper is detecting the blood hemoglobin level and glucose concentration levels in urine samples more accurately than the previously proposed whispering gallery mode (WGM) and photonic crystal nanocavity based optical sensors.