Abstract: The sonic black hole (SBH) absorber consists of an acoustic metamaterial structure formed by partitions arranged symmetrically along its central axis, with partition lengths varying exponentially toward both ends. Within this structure, the speed of sound gradually decreases, producing an acoustic black hole effect. Ideally, incident sound waves would experience no reflection, resulting in perfect absorption. However, the actual acoustic performance of SBH absorbers is limited by truncation effects and manufacturing imperfections, necessitating the incorporation of damping material to achieve satisfactory absorption. This study begins with a theoretical analysis of the acoustic behavior of the SBH absorber. Subsequently, various layout schemes for the damping material are designed and evaluated. Simulation results indicate that sound pressure concentrates in the 1st through 5th gaps at the bottom of the SBH absorber—identifying these gaps as the optimal locations for damping material placement. Finally, experimental validation is conducted. The results show that placing damping material only at the SBH terminus does not effectively enhance absorption performance. In contrast, significantly improved acoustic absorption is achieved when damping material is placed in the 1st through 5th gaps at the bottom of the SBH.