A terahertz metasurface absorber with actively switchable bandwidth enabled by vanadium dioxide (VO₂) is presented and investigated numerically. The VO₂ is a phase-change material and its conductivity in the terahertz range changes by several orders of magnitude upon phase-transition. The metasurface consists of an H-shaped fractal resonator placed on top of a polyimide spacer and a ground-plane of gold. The resonator is composed of an H-shaped level-1 fractal of gold and VO₂ strips that converts it to a level-2 fractal. At room temperatures, the VO₂ is in the insulator state and the resonator reduces to a level-1 fractal offering narrowband absorption at 8.08 THz reaching 0.98 absorption. At higher temperatures, the VO₂ is in the metallic state and the resonator is effectively a level-2 fractal with an absorption higher than 0.9 in a bandwidth of 6.63–9.89 THz.