Low-cost and easily available natural zeolite is a promising adsorbent for metal ions removal in wastewater treatment. The possibility of using zeolitic tuff from Serbia in the form of Na-enriched natural zeolite (Na-Z) for the adsorption of Pb2+, Zn2+, Cu2+, and Ni2+ ions from wastewater was investigated in the presented paper. The research included Na-Z characterization and determination of adsorption kinetics in individual ion adsorption tests using non-linear pseudo-first-order (PFO), pseudo-second-order (PSO) and mixed-order (MO) kinetic models. The results indicate that the adsorption processes of metal ions on Na-Z are complex processes dominated by multiple rate-limiting mechanisms and best defined by the MO model. The mechanisms of ion diffusion and adsorption to active sites are equally represented in the Pb2+ ions adsorption process. The mechanism of ion diffusion is more pronounced in the Zn2+ ions adsorption process, while in the case of the adsorption of Cu2+ and Ni2+ ions adsorption on the active sites is the main kinetic mechanism. Within the MO model, the PFO rate (external/internal diffusion) and the PSO rate (adsorption on the active sites) were calculated and results were applied to a multicomponent wastewater sample in order to determine and explain the adsorption efficiency in wastewater treatment. The results show that the rate of adsorption of individual metal ions and the efficiency of ion removal from a multicomponent wastewater sample are influenced by several factors including the radius of the hydrated ion and the free energy of hydration. The achieved removal of metal ions by Na-Z is Pb2+ (89%) > Cu2+ (72%) > Zn2+ (61%) > Ni2+ (58%) and defines Na-enriched natural zeolite as an effective adsorbent in wastewater treatment.