A strong chiral near-field plays significant roles in the detection, separation and sensing of chiral molecules. In this paper, a simple and symmetric metasurface is proposed to generate strong chiral near-fields with both circularly polarized light and linearly polarized light illuminations in the mid-infrared region. Owing to the near-field interaction between plasmonic resonant modes of two nanosheets excited by circularly polarized light, there is a strong single-handed chiral near-field in the gap between the two graphene nanosheets and the maximum enhancement of the optical chirality could reach two orders of magnitude. As expected, the intensity and the response wavelength of the chiral near-fields could be controlled by the Fermi level and geometrical parameters of the graphene nanosheets, as well as the permittivity of the substrate. Meanwhile, based on the interaction between the incident field and scattered field, the one-handed chiral near-field in the gap also could be generated by the linearly polarized light excitation. For the two cases, the handedness of the chiral near-field could be switched by the polarized direction of the incident light. These results have potential opportunities for applications in molecular detection and sensing. [ABSTRACT FROM AUTHOR]