A switchable metamaterial with bifunctionality of absorption and electromagnetically induced transparency is proposed based on the phase-transition characteristic of phase change material-vanadium dioxide. When vanadium dioxide is in the metallic state, an isotropic narrow absorber is obtained in the terahertz region, which consists of a top metallic cross, a middle dielectric layer, and a bottom vanadium dioxide film. By adjusting structure parameters, perfect absorption is realized at the frequency of 0.498 THz. This designed narrow absorber is insensitive to polarization and incident angle. Absorptance can still reach 75% for transverse electric polarization and transverse magnetic polarization at the incident angle of 65∘. When vanadium dioxide is in the insulating state, the top metallic cross will interact with the bottom split ring resonator, and the interaction between them will lead to the appearance of electromagnetically induced transparency. The behavior of electromagnetically induced transparency works well for transverse electric polarization and transverse magnetic polarization at the small incident angle. The designed hybrid metamaterial opens possible avenues for achieving switchable functionalities in a single device.