This research applies acoustic topology optimization (ATO) for noise barrier design with rigid and porous materials. Many researchers have investigated the pressure attenuation phenomena of noise barriers under various geometric, material, and boundary conditions. To improve the pressure attenuation performance of noise barriers, size and shape optimization have been applied, and ATO methods have been proposed that allow concurrent size, shape, and topological changes of rigid walls and cavities. Nevertheless, it is unusual to optimize the topologies of noise barriers by considering the pressure attenuation effect of a porous material. The present research develops a new ATO considering both porous and rigid materials and applies it to the discovery of optimal topologies of noise barriers composed of both materials. In the present approach, the noise absorption characteristics of porous materials are numerically modeled using the Delany–Bazley empirical material model, and we also investigate the effects of some interpolation functions on optimal material distributions. Applying the present ATO approach, we found some novel noise barriers optimized for various geometric and environmental conditions.