Black phosphorus(BP) is a kind of two-dimensional (2D) material with direct bandgap. Its adjustable bandgap fills the gap between graphene and transition metal dichalcogenides(TMDCs). At the same time, the black phosphorusalso has a higher charge carrier mobility. The unique fold-like crystal structure of the black phosphorus leads to in-plane anisotropy and it makes the photoelectric response anisotropic. It shows that the properties of black phosphorus can be dynamically adjusted by various methods. These characteristics make black phosphorus a two-dimensional material with great potential applications in the visible light to mid-infrared region and even terahertz bands. In view of this, this paper focuses on the magneto-optical response of black phosphorus. In this paper, we design a magneto-optical device in Au grating/black phosphorus/silicon hybrid plasmonic structures. The inducing of abnormal transmission through the metal grating significantly enhances the transmittance, while the Faraday rotation effect is enhanced through the mode coupling between the TE and TM in the THz range. The rigorous coupled wave analysis (RCWA) is used to calculate the transmittance of the grating. The finite element software COMSOL Multiphysics is used to calculate the transmittance and simulate the electric field distribution of the magneto-optical device. Under the optimal parameters, the Faraday rotation can increase 14.434 times, reaching to 2.7426°, and the transmittance is more than 85% with an external magnetic field of 5 T at the operation frequency (1.5 THz). We plot the electric profiles of the magneto-optical device with and without BP to prove that the Faraday rotation is a result of the magneto-optical property of the monolayer phosphorus and that the enhancement is due to the mode coupling between the TE and TM. Moreover, we extract the tunable character of the magneto-optical device with the external magnetic field and the carrier density of the black phosphorus. The external magnetic field can effectively tune the Faraday rotation angle while keeping the working wavelength and the transmittance substantially unchanged. The increasing of the carrier density will not improve the Faraday rotation angle, for the changes in surface conductivity under fixed structural parameters will disrupt the mode coupling. At the same time the transmittance will decrease, because the larger carrier density will enhance the absorption of the BP. Therefore, to obtain a higher FR angle with apparent transmittance, the carrier density should not be too high. Finally, the effects of the spoof surface plasmons on the waveguide mode and the Faraday magneto-optical effect are also discussed.