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This study provided a theoretical insight for designing novel plasmonic biosensors using bismuth selenide (Bi₂Se₃)-Graphene heterostructures. It was a van der Waals (vdWs) stacked configuration composed of gold (Au) film, few quintuple layer (QL) Bi₂Se₃ and few-layered graphene. In particular, the proposed biosensor was created by Goos-Hänchen (GH) shift rather than phase, resulting in a more sensitive biosensing response. Under the excitation of 632.8 nm, significant sensitivity enhancement performance was obtained via varying the thickness of Bi₂Se₃-Graphene heterostructures. The best configuration was 32 nm Au film−2-QL Bi₂Se₃-3-layer graphene, generating the largest GH shift, as high as −1.0202 × 10⁴ µm. Moreover, the highest detection sensitivity was determined to be 8.5017 × 10⁶ µm/RIU, responding to a tiny refractive index (RI) change of 0.0012 RIU (RIU, refractive index unit). More importantly, our proposed biosensor has shown a theoretical feasibility of monitoring virus samples. For example, there was an efficient linear detection range for severe acute respiratory syndrome coronavirus 2 (SARS-CoV−2, 0~13.44 nanomole (nM)) and its Spike (S) glycoprotein (0~59.74 nM), respectively. It is expected that our proposed plasmonic biosensor has a potential application in performing sensitive detection of SARS-CoV−2.