Black phosphorus (BP) is an important two-dimensional material that plays a key role in new photoelectric devices. In this work, a triple-band BP-based absorber was proposed, in which a monolayer BP is coupled with the missing angle rectangular structure. Due to the critical coupling of the guided resonance, the BP absorber achieves a triple-band absorption. The results showed that the absorption spectra at 2901.76 nm, 3810.71 nm, and 4676.97 nm under TM polarization achieve a high absorption of 95.45%, 98.68%, and 98.06%, respectively. In addition, the absorption peak and resonance wavelength can be flexibly adjusted by the electron doping of BP, the geometrical parameters of the structure, and the refractive index of the dielectric substrate. Because of the anisotropy properties of BP, the structure exhibits polarization-dependent absorption characteristics. Thus, the missing angle rectangular structure will provide a potential to design mid-infrared absorbers and shows a significant practical application in many photoelectric devices such as photodetectors, modulators, and optical switches.