Peracetic acid (PAA) can be activated to generate various radicals to degrade organic contaminants and holds great promise in wastewater treatment. Herein, a novel nano-sized magnetic spinel structured FeCo₂O₄ catalyst was synthesized by sol-gel method. It showed excellent performance in activating PAA for sulfamethoxazole (SMX) degradation. Acetyl(per)oxyl radicals (CH₃C(O)O^• and CH₃C(O)OO^•) were identified as the major reactive species attacking SMX. Surface chemistry characterization in combination with theoretical computation revealed that the catalytic activity of FeCo₂O₄ stems from the Co(II)/Co(III) cycling. PAA activation occurs on the FeCo₂O₄ (220) plane with higher adsorption energy (-5.10 eV) and d-band center (-1.56 eV). Although the Fe(III) in FeCo₂O₄ does not activate PAA directly, it increases the adsorption of PAA on the reaction plane and facilitates charge transfer, thus enhancing the activation. This work contributes to the understanding and rational designing of spinel-like Co-based materials for PAA-based water treatment.