We investigate theoretically the strong coupling between surface plasmon resonances (SPRs) and absorption bands of hemoglobin. When the surface plasmon resonance spectrally overlaps the absorption bands of hemoglobin, the system is strongly coupled and its dispersion diagram exhibits an anti-crossing. Working in the conditions of strong coupling enhances the sensitivity of a SPR sensor up to a factor of 10. A model for the permittivity of hemoglobin, both in oxygenated and deoxygenated states, is presented and the study is carried out for both angle and wavelength modulated SPR sensors. Finally, a differential measurement is shown to increase the sensitivity further.