In order to realize dual-band perfect absorption in the infrared wavelength range, single-layer black phosphorus ribbons were arranged in parallel with alternating carrier doping concentration. Theoretical analysis and optical simulation were performed to get absorption spectra and sensing characteristics of the device in the infrared wavelength range. The results show the proposed device can achieve dual-band perfect absorption (>99.9% absorption efficiency) in the 2 μm~5 μm infrared wavelength range. The high absorption is caused by the critical coupling of incident light to the device, and instructive resonance is formed; the on-resonance light is restricted around black phosphorus; the dual-band absorption characteristic of the metamaterial makes it an ideal sensor with high reliability and accuracy; shift of absorption peaks is almost in a linear relationship with change of refractive index of cladding material. The margin of error between the calculated and actual refractive index is within 1%. The simple structure and reasonable tolerance in dimension deviation make the proposed metamaterial a good candidate for applications such as multiple-band absorption and sensing in the infrared wavelength range.