We theoretically present a high-efficiency switchable reflective terahertz polarization converter composed of a periodic array of rectangular-shaped metal-dielectric-graphene sandwich structure on a dielectric substrate supported by a thick metallic film. Graphene sheet together with the rectangular-shaped metal patch provides tunable anisotropic hybrid magnetic plasmon resonance to obtain tunable phase delay of 90° and 180°, corresponding to a quarter-wave plate (QWP) and half-wave plate (HWP), respectively. Results of numerical simulations indicate that the proposed structure can switch functions between a QWP and HWP at a certain frequency simply by adjusting the Fermi energy of graphene. Both the QWP and HWP have high energy conversion efficiency, respectively 83% and 90% at 15.96THz, and high polarization conversion ratio closed to 1.