In this work, we propose a multi-functional broadband terahertz polarization converter based on graphene-VO2 hybrid metamaterial, which can switch between transmissive linear-to-linear conversion and reflective linear-to-circular conversion. The function of the metamaterial can be controlled by both the temperature and the Fermi energy of the graphene. At 298K, the metamaterial converts the y-polarized wave into x-polarized wave in 0.39-1.22THz. In the meanwhile, changing the Fermi energy of graphene, the converted polarization angle can be tuned from 90° to 45°. Increasing the temperature to 358K, the incident linearly polarized wave is reflected into circularly polarized wave. On this condition, tuning the Fermi energy, the metamaterial can separately convert the linear polarization wave into left-circularly polarized wave in 1.57-2.74THz and right-circularly polarized wave in 1.13-1.59THz. Such a switchable multi-functional broadband polarization converter may achieve potential applications in compact terahertz devices and integrated terahertz circuits.