Aiming at reducing the high-amplitude and wide-frequency noise in charged air intake system of the powertrain, this paper proposes a new method for predicting the acoustic characteristics of an irregular cross-section multi-chamber perforated resonator under flow conditions. By this method, the presence of three-dimensional sound waves and the effects of higher-order modes are considered, and the acoustic performance of the resonator can be evaluated through the computation of transmission loss. Moreover, by discretizing the cross-section of the perforated resonator and extracting node information, this method can solve the acoustic characteristics of the perforated resonator with any cross section. Based on the transfer matrix method, the quadrupole parameters of each chamber are obtained. Then, the acoustic characteristics of the multi-chamber perforated resonator could be calculated. The theoretical prediction data and the experimental data have been compared, and the results show good agreement within the entire frequency range, which verifies the accuracy of the theoretical prediction approach. Based on this prediction approach, the influence of section ratio, structure parameters, and inlet flowrate on the acoustic characteristics of the resonator is explored. The results show that when the structural parameters change, the peak resonance frequency of the resonator will have a regular shift. With the increase of the inlet flowrate, the main frequency band of sound attenuation will decrease significantly. The theoretical method developed in this work can be used for the calculation and optimization of multi-chamber resonators in various applications.