We present and numerically verify a functionally hybrid dual-mode tunable polarization conversion metasurface based on graphene and vanadium dioxide (VO2). The tunable polarization converter consists of two patterned graphene layers separated by grating which is composed of gold and VO2. Due to the existence of phase change material VO2, the polarization conversion mode can be switched flexibly between the transmission and reflection modes. Theoretical calculations show the proposed polarization conversion metasurface can obtain giant asymmetric transmission (AT) at 0.42 and 0.77 THz when VO2 is in the insulating state. Conversely, when VO2 is in the metallic state, the converter switches to the reflection mode, demonstrating broadband polarization conversion for both forward and backward incidences. Furthermore, the conductivity of graphene can be modulated by changing the gate voltage, which allows dynamic control polarization conversion bandwidth of the reflection mode as well as the AT of the transmission mode. The robustness of the metasurface has also been verified, the high polarization conversion efficiency and AT can be maintained over wide incidence angles up to 65° for both the xoz plane and yoz plane. These advantages make the proposed hybrid tunable polarization conversion metasurface a promising candidate for THz radiation switching and modulation.