Graphene-based absorbers are highly valued in terahertz technology due to their efficient performance. In this study, we theoretically propose a tunable, high sensitivity, single-band terahertz perfect absorber with polarization coherence that exhibits stable performance across a broad range of incidence angles. Simulation results show that the absorber's sensitivity to both TM and TE waves can be maintained at about 2 THz/RIU, with optimal values above 13.3 RIU−1 for TM waves and 12.9 RIU−1 for TE waves, and all Q-factors above 52. Furthermore, the impedance matching approach is utilized to explain the mechanism underlying its efficient absorption, and the electric field distribution is used to analyze the polarization coherence phenomena. We also propose a polarization-insensitive hetero-geometric structure based on the original structure, which allows for the separation of the absorption peaks by adjusting the geometrical parameters. These results show that the structure has a wide range of applications in aerospace, communication engineering, and image processing.