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We propose and numerically demonstrate a tunable plasmon-induced transparency (PIT) phenomenon based on asymmetric H-shaped graphene metamaterials. The tunable PIT effect is realized through varying the applied polarization angles rather than changing the structure geometry. By simply adjusting the polarization angle, the transmission spectra can be controlled between the switch-on state and switch-off state. The physical mechanism of the induced transparency is revealed from magnetic dipole inductive coupling and phase coupling. Importantly, by varying the Fermi energy of the graphene or the refractive index of the substrate, the resonant position of the PIT can be dynamically controlled and the maximum modulation depths can reach up to 60.7%. The sensitivity (nm/RIU) of the graphene structure, which is the shift of resonance wavelength per unit change of refractive index, is 5619.56 nm/RIU. Moreover, we also extend our research to the x-axis symmetric H-shaped structure, and the tunable PIT transmission window can also be realized. The physical mechanism of the induced transparency is revealed from the electric dipole hybridization coupling. Our designed H-shaped graphene-based structures is a promising candidate for compact elements such as tunable sensors, switches and slow-light devices. [ABSTRACT FROM AUTHOR]