The acoustic black hole has the ability to gather and manipulate the flexural wave in the structure, and can be used to achieve vibration suppression of the structure. A group of FEM models for the vibration analysis of the rectangular plate embedded with acoustic black holes were established in this paper. Four monitoring points on the ABH plate were selected to calculate their vibration velocity response in 100 Hz-3 kHz frequency interval. In order to study the effects of acoustic black hole geometric parameters and damping layer geometric parameters on the vibration response of the ABH plate, 15 combinations of different parameters of the maximum ABH diameter, the truncated thickness of the ABH, the power index of the ABH, and the damping layer thickness, the maximum diameter of the damping layer were selected to calculate the vibration velocity response of the four monitoring points. The calculation result can help us understand the effects of acoustic black hole geometric parameters and damping layer geometric parameters on the vibration suppression of rectangular plate.