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Black phosphorus (BP), as a two-dimensional material, has exhibited unique optoelectronic properties due to its anisotropic plasmons. In the present work, we theoretically propose a radiative thermal switch (RTS) composed of BP gratings in the context of near-field radiative heat transfer. The simply mechanical rotation between the gratings enables considerable modulation of radiative heat flux, especially when combined with the use of non-identical parameters, i.e., filling factors and electron densities of BP. Among all the cases including asymmetric BP gratings, symmetric BP gratings, and BP films, we find that the asymmetric BP gratings possess the most excellent switching performance. The optimized switching factors can be as high as 90% with the vacuum separation d=50 nm and higher than 70% even in the far-field regime d=1 µm. The high-performance switching is basically attributed to the rotatable-tunable anisotropic BP plasmons between the asymmetric gratings. Moreover, due to the twisting principle, the RTS can work at a wide range of temperature, which has great advantage over the phase change materials-based RTS. The proposed switching scheme has great significance for the applications in optoelectronic devices and thermal circuits.