Owing to the outstanding physical properties of graphene, its biosensing applications implemented by the terahertz metasurface are widely concerned and studied. Here, we present a novel design of the graphene metasurface, which consists of an individual graphene ring and an H-shaped graphene structure. The graphene metasurface exhibits a dual-resonance response, whose resonance frequency strongly varies with the geometrical parameters of the proposed metasurface, the carrier density of graphene, and the analyte composition. The transparency window, including width and position, can be artificially controlled by adjusting the geometrical parameters or the Fermi energy. Furthermore, the sensing parameters of the graphene metasurface for cancerous and normal cells are investigated, focusing on two factors, namely cell quantity and position on the metasurface. The simulated results clearly show that the theoretical sensitivity, figure of merit, and quantity of the graphene metasurface for breast cells reach 1.21 THz/RIU, 2.75 RIU (Formula presented.), and 2.43, respectively. Our findings may open up new avenues for promising applications in the diagnosis of cancers.