This paper demonstrates a band enhanced ultra-broadband terahertz absorber (UBTA) based on a high-impedance surface and cavity resonance; the absorber consists of a high-impedance surface and a metallic plate spaced by a dielectric spacing layer. Simulations indicate that ultra-broadband absorption over 90% from 4.65 to 8.86 THz is realized by the high-impedance surface. It is noted that the absorption is further broadened by inserting air cylinders (ACs), thus showing that the absorption rate exceeds 90% from 5.35 to 13.08 THz. The simulations also demonstrate that the UBTA can achieve high absorption under wider incident angles. Moreover, surface current, electric field distribution, and power loss density are simulated to expound the physical mechanism.