In this work, an advanced muffler design method is presented to reduce duct noise in low-frequency and mid-frequency bands simultaneously. Although internal partitions inside an expansion chamber may increase the noise attenuation performance of a muffler in mid-frequency and high-frequency bands, an optimal layout of partitions cannot be easily obtained for a low frequency band. To figure out the disadvantage, the design domain of a muffler is divided into two sub-design domains: one is for a low-frequency noise and the other is for a mid-frequency noise. The first sub-design domain is used for resonator design, and the second one is used for designing the internal partition layout in an expansion chamber with topology optimization. The optimal muffler obtained by solving the formulated design problem showed high transmission loss values not only in the low-frequency band but also in the mid-frequency band.