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This paper presents a wideband tunable cross-polarization converter based on a graphene metasurface with a hollow-carved “H” array in the mid-infrared regions. The converter consists of three layers: the upper layer of the insulation dielectric layer is a periodic regular hollow-carved “H” array, and the bottom layer is a metal ground plane. Simulation is carried out by applying the frequency domain solver of the CST Microwave Studio software. The numerical simulation results show that the polarization converter transforms linear light into its cross-polarization light. The polarization conversion ratio is over 90% at 2.53 THz within the range of 34.39 to 36.92 THz, whereas the FWHM bandwidth is 3.87 THz within the range of 33.8 to 37.67 THz, about 11% of the central frequency. Thus, the cross-polarization converter can be dynamically tuned over a wide frequency range by altering the Fermi-energy of graphene, without reoptimizing and refabricating nanostructures. The operating frequency band of the proposed structure can also be tuned by changing the size of $w_1$ or $\Lambda$ while keeping the polarization conversion ratios high. Moreover, strong robustness is observed under the oblique incidence. Specifically, the polarization conversion ratios can be maintained at over 90% at angles of incidence of up to $50^\circ$ . Therefore, the proposed device has potential development and application in the manipulation of light polarization in the mid-infrared regions.