A single layer dual L-shaped graphene metasurface is presented to achieve a high operative and tunable polarization converter in the mid-infrared regime. The proposed device and numerical results indicate that linearly polarized wave can be converted to its cross-polarized wave. In addition, it can be used as a converter to a circularly polarized wave. This converter is insensitive to the angle of incident wave. Working frequencies can be easily and significantly tuned within a wide frequency range by regulating the chemical potential of the graphene. The physical procedure of the polarization conversion effect is explicated via coupling of the electric field components with various plasmon resonance modes of the metasurface. The suggested structure can pave a way to development of controllable plasmonic polarization converter systems for optical communication applications.