We propose a reflection-type infrared biosensor by exploiting localized surface plasmons in graphene ribbon arrays. By enhancing the coupling between the incident light and the resonant system, an asymmetric Fabry–Perot cavity formed by the ribbons and reflective layer is employed to reshape the reflection spectra. Simulation results demonstrate that the reflection spectra can be modified to improve the figure of merit (FOM) significantly by adjusting the electron relaxation time of graphene, the length of the Fabry–Perot cavity, and the Fermi energy level. The FOM of such a biosensor can achieve a high value of up to 36/refractive index unit (36/RIU), which is ～4 times larger than that of the traditional transmission-type one. Our study offers a feasible approach to develop biosensing devices based on graphene plasmonics with high precision.