This publication presents the results of combined theoretical and experimental research for the potential use of natural clinoptilolite zeolite (CLI) as an odor-adsorbing material. In this study of adsorption capacity, CLI of various granulation was used and its modifications were made by ion exchange using Sn and Fe metals to check whether the presence of metals as potential active centers does not lead to catalytic processes and may lead to enhanced absorption of odorous substances through their adsorption on the created metallic forms. Additionally, in order to increase the specific surface area, modifications were made in the form of hierarchization in an acidic environment using hydrochloric acid to also create the hydrogen form of zeolite and thus also check how the material behaves as an adsorbent. To compare the effect of CLI as a sorption material, synthetic zeolite MFI was also used—as a sodium form and after the introduction of metals (Sn, Fe). The above materials were subjected to adsorption measurements using odorous substances (including acetaldehyde, dimethylamine, pentanoic acid and octanoic acid). Based on the measurements performed, the most advantageous material that traps odorants is a natural material—clinoptilolite. Depending on the faction, its ability varies for different compounds. In the case of acetaldehyde, an effective material is clinoptilolite with a grain size of up to 2 mm. In the case of carboxylic acids, it is material after hierarchization with a fraction of 3–4 mm. In the case of theoretical calculations, information was obtained to show that metallic centers are more stable above oxygen, which is associated with the skeletal aluminum in clinoptilolite.