We propose a polarization-insensitive broadband tunable metamaterial-based perfect absorber with high absorption. This absorber is composed of three layers of structure, a gold substrate at the bottom, the first polyethylene cyclic olefin copolymer (Topas) dielectric and vanadium dioxide (VO₂) as the top layer. Our theoretical results led us to show that this absorber has more than 90% absorption at 3.42 to 7.22 THz with a continuous bandwidth of 3.8 THz, whereas more than 99% absorption in the range of 3.98 to 6.68 THz with a continuous bandwidth of up to 2.7 THz in the case of vertical incidence of electromagnetic waves. In addition, near-perfect amplitude modulation can be achieved by varying the conductivity of the VO₂ where the absorbance can be continuously tuned from 1.7% to 100%. It is concluded that the performance of our reported absorber is significantly improved compared to that of previously reported VO₂ absorbers. Moreover, perfect absorption and resonant frequency drift can be explained with impedance matching and propagation phase theories, respectively. In addition, our absorber has polarization insensitivity as well as wide-angle absorption due to the presence of rotational symmetry in the absorber structure. Finally, we believe that the absorber proposed is strongly competitive in the terahertz (THz) range for designing THz modulators, cloaking, optic-electro switches, and photodetector.