In this paper, we design a metasurface terahertz perfect absorber with multi-frequency selectivity and good incident angle compatibility using a double-squared open ring structure. Simulations reveal five selective absorption peaks located at 0−1.2 THz with absorption 94.50% at 0.366 THz, 99.99% at 0.507 THz, 95.65% at 0.836 THz, 98.80% at 0.996 THz, and 86.70% at 1.101 THz, caused by two resonant absorptions within the fundamental unit (fundamental mode of resonance absorption, FRA) and its adjacent unit (supermodel of resonance absorption, SRA) in the structure, respectively, when the electric field of the electromagnetic wave is incident perpendicular to the opening. The strong frequency selectivity at 0.836 THz with a Q-factor of 167.20 and 0.996 THz with a Q-factor of 166.00 is due to the common effect of the FRA and SRA. Then, the effect of polarized electromagnetic wave modes (TE and TM modes) at different angles of incidence (θ) and the size of the open rings on the device performance is analyzed. We find that for the TM mode, the absorption of the resonance peak changes only slightly at θ = 0−80°, which explains this phenomenon. The frequency shift of the absorption peaks caused by the size change of the open rings is described reasonably by an equivalent RLC resonant circuit. Next, by adjusting two-dimensional materials and photosensitive semiconductor materials embedded in the unit structure, the designed metasurface absorber has excellent tunable modulation. The absorption modulation depth (MD) reaches ≈100% using the conductivity of photosensitive semiconductor silicon (σ SI-ps ), indicating excellent control of the absorption spectrum. Our results can greatly promote the absorption of terahertz waves, absorption spectrum tunability, and frequency selectivity of devices, which are useful in the applications such as resonators, biodetection, beam-controlled antennas, hyperspectral thermal imaging systems, and sensors.