In this work, an acoustic metamaterial panel is designed for improving the noise attenuation performance of a multilayer panel. The acoustic metamaterial panel is a kind of perforated panel, one hole of which is enclosed with array of annular cavities. The hole is regarded as a circular duct consisting of unit cells; and a unit cell consists of an inlet, an expansion chamber, and an outlet. The noise-blocking frequency range of the acoustic metamaterial panel is identified from a bandgap in its dispersion curve. The effect of each part of the unit cell on the bandgap is investigated, and dominant parts are selected. The sizes of the dominant parts are determined to locate the target noise-blocking frequency range into the bandgap. The noise attenuation performance of a designed acoustic metamaterial panel is experimentally and numerically validated.