In this study, porous carbon nanocubes encapsulated magnetic metallic Co nanoparticles (denoted as Co@N-PCNC) was prepared via pyrolyzing ZIF-67 nanocubes precursor at 600 °C and characterized by various technologies. It was used to activate peroxymonosulfate (PMS) to degrade Congo red (CR) dye efficiently. Over 98.45% of 50 mg L−1 CR was degraded using 0.033 mM PMS activated by 75 mg L−1 Co@N-PCNC within 12 min. The free radical quenching experiments were performed to reveal the nature of the reactive oxygen species radicals generated throughout the catalytic oxidation of CR. The effects of common inorganic anions and the water matrix on CR removal were studied. Moreover, the results of the kinetic study revealed the suitability of the pseudo-first-order and Langmuir–Hinshelwood kinetic models for illustrating CR degradation using the Co@N-PCNC/PMS system. Ultimately, the Co@N-PCNC displayed good operational stability, and after five cycles, the CR removal rate can still maintain over 90% after 12 min.