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Environmentally friendly magnetic sodium alginate beads with glutaraldehyde cross-linking catalyzed by acetic acid-hydrochloric acid were successfully designed (FSSi@SA), and the magnetic bio-sorbents after amide reaction (FSSi@SA-sula) were utilized to absorb fluoroquinolone antibiotics in water. After amidation, FSSi@SA-sula exhibited strong pH adaptability (pH = 6.0–12.0). Langmuir and pseudo-first-order models can better describe the isotherm and kinetic process well, respectively. Under the optimization conditions with pH = 7 and temperature of 318.15 K, the maximum adsorption capacities of FSSi@SA-sula on the third-generation FQs ciprofloxacin (CIP) and the fourth-generation FQs moxifloxacin (MOX) respectively reached 365.66 and 149.57 mg g−1. The thermodynamics research indicated that the as-prepared FSSi@SA-sula is spontaneous and feasible. And after five adsorption cycles, the loss of adsorption capacity was less than 20% for both CIP and MOX, demonstrating the fine reusability and stability of the designed magnetic bio-sorbent. This study provides some ideas for facile synthesis of acid-catalyzed sodium alginate-glutaraldehyde cross-linking, which has promising applications in grafting various types of groups onto the retained carboxyl groups of sodium alginate spheres for the various contaminants removal in wastewater. [Display omitted] • FSSi@SA-sula beads were prepared by acid-catalyzed glutaraldehyde cross-linking. • FSSi@SA-sula showed excellent adsorption and reusability for CIP and MOX. • Langmuir and pseudo-first-order models better fitted adsorption process. • The mechanisms include electrostatic interactions, hydrogen bonding and n-π EDA. • Provided new ideas for facile synthesis of functional sodium alginate adsorbents. [ABSTRACT FROM AUTHOR]