As a new type of efficient wave control technology, the ABH (Acoustic Black Hole) phenomenon is widely used in vibration control of beam and plate structures. However, the traditional acoustic black hole structures have many shortcomings, such as weak local strength and stiffness, large feature size and high effective frequency, which limit the further application and promotion of acoustical black hole technology. A novel acoustic black hole absorber (ABHA) is designed. In this paper, the finite element simulation method is used to study the energy focusing effect of the ABHA. The results show that it has high energy focusing efficiency. By analyzing the energy focusing effect of ABHA under different cut-off thicknesses, it proves that that a smaller cut-off thickness is beneficial to improve the energy focusing effect of ABHA in the middle and high frequency bands.