Borophene has the unique optical properties of two-dimensional materials and its own anisotropic characteristics. This work proposes a perfect narrow-band absorption structure to enhance the interaction of light with the monolayer borophene inserted into two different dielectric gratings. The structure efficiently improves absorption efficiency based on the quasi-bound states in the continuum (Q-BIC). The absorption characteristics are numerically simulated and theoretically analyzed by using the rigorous coupled-wave analysis (RCWA) method and the finite element method (FEM). The absorption efficiency of the monolayer borophene is high, up to 99.18% with a full-width at half maximum (FWHW) of 0.62 nm, achieving nearly perfect narrow-band absorption. Moreover, the mechanism of enhanced absorption of monolayer borophene is verified by the coupled mode theory (CMT), which indicates that the nearly perfect absorption is also derived from the critical coupling. At the same time, the influence of the thickness and width of the two layer dielectric structure on the absorption efficiency is theoretically analyzed. Furthermore, due to the anisotropic optical properties of the structure for TE and TM polarized light, a narrow-band polarization plate or sensor can be realized. The structure designed provides a new possibility to enhance the interaction between monolayer borophene and light.