Abstract: The structure of acoustic cloaking covering has an important effect on the cloaking performance. In this paper the acoustic field distribution and average visibility of different cloaking covering structures are calculated and compared. The results show that the total thickness, the number of layers and the thickness arrangement of the acoustic cloaking covering have different effects on cloaking performance. When the layer thickness is determined, the greater the total thickness, the better the cloaking performance; when the total thickness is determined, the more layers lead to the better cloaking performance; and when the total thickness and the number of layers are determined, the arrangement of decreasing layer thickness from inner to outer will have better cloaking performance than the arrangement of increasing layer thickness from inner to outer and the arrangement of equal layer thickness. The calculation results in this paper have some reference value for the design and application of the acoustic cloaking covering.