The acoustic black hole (ABH) effect is a phenomenon in which the thickness of the beam or the plate is tailored in accordance with the power law, so that the speed of the bending wave at the tip of the structure is reduced to zero, resulting in that no reflection occur. In this paper, a finite element model is established based on the plate with acoustic black hole. The influence of the power index, the central cut-off thickness and the position on the vibration control of the plate is analyzed based on the energy band theory in the frequency domain. A model of acoustic black hole plate containing stiffeners is established in order to overcome the weakening of acoustic black hole plate. The influence of the stiffeners on the rigidity and vibration control of the plate is investigated. The experiment is carried out to verify the effect of the stiffeners on vibration control of a plate with acoustic black hole. The theoretical and experimental results show that the stiffeners enhance the rigidity of the plate effectively and an excellent vibration control is still achieved in the high frequency range above 4000 Hz. This provide a reference for the application of acoustic black hole in engineering, especially for the weakening of the plate with acoustic black hole.