Noise has a negative impact on our environment and human health. For this reason, it is necessary to eliminate excessive noise levels. This paper is focused on the study of the sound absorption properties of materials with open-porous structures, which were made of acrylonitrile butadiene styrene (ABS) material using additive technology. Four types of structures (Cartesian, Octagonal, Rhomboid, and Starlit) were evaluated in this work, and every structure was prepared in three different volume ratios of the porosity and three different thicknesses. The sound absorption properties of the investigated ABS specimens were examined utilizing the normal incidence sound absorption and noise reduction coefficients, which were experimentally determined by the transfer function method using a two-microphone acoustic impedance tube. This work deals with various factors that influence the sound absorption performance of four different types of investigated ABS material’s structures. It was found, in this study, that the sound absorption performance of the investigated ABS specimens is strongly affected by different factors, specifically by the structure geometry, material volume ratio, excitation frequency of an acoustic wave, material’s thickness, and air space size behind the tested sound-absorbing materials.