In this work, a double-layer honeycomb microperforated structure with adjustable back-cavity’s height is designed based on cylinder honeycomb structure and microperforated panel (MPP). The sound absorption performance can be changed by adjusting the height of back-cavity. Thus, a better absorption performance is achieved by changing the position of the inner MPP. Acoustic impedance of the structure was calculated based on transfer matrix method. The sound absorption coefficient of the structure was obtained by finite element method (FEM). Meanwhile, the 3D printing technology was used to produce the experimental samples. The experimental results demonstrate that the sound absorption coefficient of the structure is greater than 0.8 in the range of 750–1250 Hz, greater than 0.9 in the range of 2297–3592 Hz, and above 0.5 in the range of 500–4000 Hz. In addition, the feasibility of achieving adjustable sound absorption by means of changing the height of the back-cavity is verified by theoretical, simulation, and experimental results. The structure proposed in this work can realize the function of wide-band and better sound absorption performance by changing the position of the inner MPP, which can be applied to effectively reduce different frequencies noise.