In recent years， acoustic black hole （ABH） has shown an extremely broad application prospect in the fields of structural vibration and noise suppression， acoustic wave control， energy recovery， etc， due to its excellent performance. However， the trun? cation of ABH edge will lead to the existence of non-zero reflection coefficient， thus weakening the acoustic black hole effect. In this paper， the constrained layer damping is introduced into ABH plates. Under the framework of Rayleigh Ritz method， Gaussian function is selected as the basis function， and the distribution of basis function is determined according to the shape of ABH plate to avoid the singularity of mass matrix and stiffness matrix. A semi analytical model of ABH plate with constrained layer damping is established. By comparing with the results of finite element analysis， the correctness of the semi analytical modeling method is veri? fied. The influence of structural parameters of constrained layer damping on the bending vibration characteristics of ABH plate is studied， and the damping mechanism and energy dissipation of constrained layer damping are revealed. The experiment further veri? fies the damping effect of ABH plate with constrained layer damping. The research provides a design reference for the application of constrained layer damping in ABH structures.