In this paper, we propose a multi-layer micro-perforated panel structure based on a curled space for broadband sound absorption at low frequencies, which increases the number of perforated panel layers in a limited space using a curled space. The absorption coefficients of the structure under plane wave conditions were calculated using the transfer matrix method and the finite element method. It is demonstrated that the multilayer micro-perforated panel structure can ensure high absorption (consistently over 90%) in the frequency range of 400~5000 Hz. The sound absorption mechanism of the multi-layer micro-perforated panel structure is investigated by using the acoustic impedance along with the reflection coefficient of the complex frequency surface. In addition, we also discuss the effects of the micro-perforated panel parameters on the structural sound absorption coefficient. The results show that the proposed multi-layer micro-perforated panel structure provides an excellent solution for sound absorption in a limited space.