A multilayer metamaterial with switchable functionalities is presented based on the phase-transition property of vanadium dioxide. When vanadium dioxide is in the metallic state, a broadband absorber is formed. Calculated results show that the combination of two absorption peaks enables absorptance more than 90% in the wide spectral range from 0.393 THz to 0.897 THz. Absorption performance is insensitive to polarization at the small incident angle and work well even at the larger incident angle. When vanadium dioxide is in the insulating state, the designed system behaves as a narrowband absorber at the frequency of 0.677 THz. This narrowband absorber shows the advantages of wide angle and polarization insensitivity due to the localized magnetic resonance. Furthermore, the influences of geometrical parameters on the performance of absorptance are discussed. The proposed switchable absorber can be used in various applications, such as selective heat emitter and solar photovoltaic field.