In this paper, four different configurations of sensitive biosensors based on graphene-plasmonic combinations are designed and proposed. The nanostructures are made of graphene, SiO2, aluminum and gold layers on a silicon substrate. Graphene-ring shaped structures with diagonal strips in vertical and horizontal directions are considered in the structures which greatly affect the absorption characteristics (absorption peak value and wavelength). Aluminum layer is used in the structure to prevent the transmission of light throughout some layers and improving the absorption factor. To promote the functionality of the structures, effects of the structural parameters (R1 and R2) and chemical potentials (Ef1, Ef2, Ef3 and Ef4) on the absorption peak-wavelength and its value, are also studied. The four individual configurations with different layers and strip directions demonstrate distinct and different wavelength ranges; structure-1: 45-60 µm, structure-2: 50-70 µm, structure-3: 70-85 µm, and structure-4: 80-100 µm. Thus, they can be utilized for wide categories of applications. Sensitivities of 1500nm/RIU, 2250/RIU, 3750nm/RIU and 4850nm/RIU are obtained for four types, respectively. The proposed structures indicate more sensitivities and they can be used in acceptable sensing characteristics for different applications like hemoglobin and glucose concentrations in blood samples and can be utilized as refractive index bio-sensing sensors.