The universality and stability are significant for efficient environmental catalysts. Herein, a series of g-C3N4 supported ZnO/Co3O4 nanocomposites (ZCO-CN) were constructed through the one-pot pyrolysis method. The constructed ZCO-CN composites showed superior properties in peroxymonosulfate (PMS) activation to degrade tetracycline (TC) with remarkable universality and stability. It has been able to accommodate common anions and cations and a wide pH range (3−11) in the real wastewater system with a removal rate of 91% within 5 min. After 5 cycles, the degradation rate can still be maintained at 83.8%. Moreover, ZCO-CN still displayed outstanding catalytic performance for methyl orange and oxytetracycline. The singlet oxygen (1O2) and superoxide radicals (∙O2-) during the TC degradation process are confirmed through quenching experiments and electron paramagnetic resonance (EPR) analysis. The abundant N in the support of g-C3N4 can form interactions with ZnO/Co3O4 (ZCO) facilitating the formation of oxygen vacancies, which promotes the formation of 1O2, inhibits the leaching of metal ions and significantly enhances the stability of the catalyst. This work proposes an immobilized ZnO/Co3O4/g-C3N4 with enhanced catalytic performance, high universality, and stability for PMS activated toward pollution removal.