Acoustic Black Holes (ABH), a new method of passive vibration damping, have received much interest recently due to their lightweight and economically efficient properties. This paper aims to establish the optimal shape of the damping layer treated on ABH under harmonic loading. Firstly, a validation of numerical scheme that is used throughout this paper is carried out. A good agreement of the numerical simulation and the experiment is shown. Then, a numerical study of ABH with different dimensions of damping layer treated is performed. It is shown that treating the whole surface of ABH with damping layer is not necessary since only a small portion of damping layer near the tip is responsible for most of the vibration absorption. Future areas of application of the optimized ABH include lightweight damping of vehicle panels such as cars, trains, ships and airplanes.