In view of the fact that most invisibility devices focus on linear polarization cloaking and that the characteristics of mid-infrared cloaking are rarely studied, we propose a cross-circularly polarized invisibility carpet cloaking device in the mid-infrared band. Based on the Pancharatnam–Berry phase principle, the unit cells with the cross-circular polarization gradient phase were carefully designed and constructed into a metasurface. In order to achieve tunable cross-circular polarization carpet cloaks, a phase change material is introduced into the design of the unit structure. When the phase change material is in amorphous and crystalline states, the proposed metasurface unit cells can achieve high-efficiency cross-polarization conversion, and reflection intensity can be tuned. According to the phase compensation principle of carpet cloaking, we construct a metasurface cloaking device with a phase gradient using the designed unit structure. From the near- and far-field distributions, the cross-circular polarization cloaking property is confirmed in the broadband wavelength range of 9.3–11.4 µm. The proposed cloaking device can effectively resist detection of cross-circular polarization.