Iron and manganese, among the most abundant elements on earth, enter bodies of water in the solution form through acid rain. High content of these metals causes sediment, turbidity, taste, and color in the water, thus leading to adverse effects on human health and quality of treated water. In this study, tea leaves and rice straw were used to remove iron and manganese from running water in a fixed-bed column. The effects of the flow rate, sorbent doses, pH, temperature, and the initial concentration of iron and manganese ions were studied. The breakthrough curve and mathematical models, including neural network, genetic algorithm, Thomas and Adams-Bohart models, were drawn upon to evaluate the results. According to the results, the best adsorbent performance was obtained at Initial concentration: 5mg/l, flow rate: 10ml/min, pH: 7.9, Adsorbent dosage: 0.1mg, Retention Time: 20-150min and Temperature: 30°C. The percentage of the removed adsorption was 87.7 and 81.3 for rice straw and tea leaves for iron removal and 83.1 and 72.1% for manganese, respectively. The adsorption capacity of rice straw is greater than that of tea leaves, and rice straw absorbs more iron ions than manganese.