In this letter, we have proposed a bi-functional switchable broadband polarization converter based on the hybrid graphene-metal metasurface. Turning the bias voltage to change Fermi level Ef from 0 to 1.0 eV, the metasurface can switch between quarter-wave plate (QWP) and half-wave plate (HWP) in the frequency band 1.38-1.72 THz. Besides, the metasurface simultaneously works as a broadband QWP and HWP in different frequency range when Ef = 1.0 eV. In addition, when Ef is in the range of 0.3 eV-0.6 eV, the metasurface can work as bi-functional broadband QWP in different frequencies as well. The physical mechanism of the bi-functional polarization converter can be explained by the electric field amplitude distributions. What's more, we find that the metasurface can work well with a tolerance to the incident light polarization angle of about ± 12.5°, which can also change the converted wave from RHCP to LHCP with the incident polarization angle change of 90°. The hybrid metasurface with the advantages of switchable bi-functions, wide operating bandwidth, and ultra-thin thickness, may achieve potential applications in tunable devices for terahertz communications.