In order to improve low-frequency characteristics of micro-perforated panel absorbers, sound absorption structures composed of micro-perforated panels and expansion chambers are design, and an optimization design method is constructed based on the transfer function model and the simulated annealing algorithm. First, a single-chamber structure composed of a micro-perforated panel and an expansion chamber is build, and the sound absorption curve is simulated by the finite element method. Second, for the sake of enlarging the continuous absorption bandwidth with absorption coefficients not less than 0.8, a three-chamber structure is designed, which has a sound absorption bandwidth of 1277Hz (27-1304Hz) covering 5.6 octave bands. Then, the transfer function model of the structure is established, and a series of theoretical formulae are derived to calculate the absorption coefficients. Subsequently, the sound absorption bandwidths calculated by the theoretical formulae and the finite element method are compared, and the relative error is 3.68%. Finally, an optimization design method is constructed by combining the transfer function model and the simulated annealing algorithm, where the optimization objective is to maximize the absorption bandwidth and the optimization variables are structural parameters of the three-chamber structure. The results show, after optimization, the three-chamber structure exhibits an excellent sound absorption performance, with a continuous bandwidth of 1591Hz (4-1595Hz), realizing 8.6 octave bands.