In this paper, we design and study a double-band anisotropic black phosphorus (BP)-based absorber. The proposed absorber is consisting of a monolayer black phosphorus, a crystalline silicon layer, and a perfect electrical conductor (PEC). Numerical results show that the absorber has two absorption peaks both close to perfect absorption, generated due to strong magnetic resonance modes. Absorption can be adjusted by varying key parameters, such as length, width, thickness, angle of incidence, and polarization angle. Two conventional parameters, sensitivity (S), and figure of merit (FOM) are used to estimate the sensing performance, the sensitivity of the absorber can be as high as 0.46THz/RIU for one peak, while 0.44THz/RIU for another peak (RIU is the unit of the refractive index). Meantime, we also calculated the concentration sensing sensitivity, and a maximum 6.4 x 10(-5)THZ/g/L is achieved. The proposed BP-based double-band absorber provides a basis for designing borophene-based sensor and other electronic-photonics devices.