Advanced oxidation processes (AOPs) always rely on the generation of inorganic radicals (e.g., HO) for contaminant destruction. Herein, we report a novel AOP, i.e., Co3O4/peracetic acid (PAA) to degrade contaminants with organic radicals at neutral pH. Using orange G (OG) as a representative, studies show that Co3O4 can effectively activate PAA to promote rapid degradation of OG at neutral pH, with extremely low cobalt leaching. Moreover, Co3O4 exhibits high structural and chemical stability in PAA activation. X-ray photoelectron spectroscopy (XPS) analysis indicated the recycling of Co2+/Co3+, and thus confirmed a catalyst role of Co3O4 in the activation of PAA. Electron paramagnetic resonance (EPR) technique and radical-quenching studies showed that organic radical species, (i.e., CH3C(O)O and CH3C(O)OO) played a critical role in the degradation process. A wide range of contaminants were further tested for their degradation in the PAA/Co3O4 system, and this system was found to exhibit certain selectivity for organic contaminants, especially for those with electron-rich functional groups/moieties, e.g., fluoroquinolones and sulfonamides. This work provides a promising strategy for the degradation of organic contaminants in water treatment.