We present a simple dual band absorber design and investigate it in the terahertz (THz) region. The proposed absorber works in dual operating bands at 5.1 THz and 11.7 THz. By adjusting the graphene chemical potential, the proposed absorber has the controllability of the resonance frequency to have perfect absorption at various frequencies. The graphene surface plasmon resonance results in sharp and narrow resonance absorption peaks. For incident angles up to 8°, the structure possesses near-unity absorption. The proposed sensor absorber’s functionality is evaluated using sensing medium with various refractive indices. The proposed sensor is simulated for glucose detection and a maximum sensitivity of 4.72 THz/RIU is observed. It has a maximum figure of merit (FOM) and Quality factor (Q) value of 14 and 32.49, respectively. The proposed optimal absorber can be used to identify malaria virus and cancer cells in blood. Hence, the proposed plasmonic sensor is a serious contender for biomedical uses in the diagnosis of bacterial infections, cancer, malaria, and other diseases.