In the present study, a calcium alginate bead adsorbent was prepared from brown algae (Macrosystis pyrifera) and was used for removal of Pb+2, Cu+2, and Sb+3 ions from aqueous solutions, using a fixed bed column. The initial concentration of metal ions, mass of adsorbent, recirculation flow, hydrodynamic cavitation, and contact time were examined, and the adsorption kinetics and isotherms were systematically studied. The Taguchi five-factor methodology was used for the development at three levels of experimentation. Experiment N° 24 (concentration, 10 mg/L; flow rate, 10 mL/s; adsorbent mass, 10 g; hydrodynamic cavitation with maximum air flow, and treatment time 240 min) resulted in the maximum removal of 92%, 78%, and 16% of lead, copper, and antimony ions, respectively. The average rate constants corresponding to pseudo-second-order kinetics for lead, copper, and antimony ions were 5.3 × 10−3, 1.4 × 10−3, and 7 × 10−5 g.mg−1min−1, respectively. In the adsorption process, they closely approximate to Langmuir and Freundlich isotherms, with adsorption capacities for Pb2+, Cu2+, and Sb3+ of 7.60, 2.07, and 0.37 mg/g, respectively, with good bioadsorption affinity of Pb > Cu > Sb. It was demonstrated that the bioadsorption equipment, with proper control of the factors, achieves concentration values of lead and copper ions below the current environmental regulations. The results of these studies indicated that calcium alginate is a promising adsorbent for separating and recovering heavy metal ions from contaminated water, although further research is needed for antimony ions.