Heterogeneous catalysts are fascinating for advanced oxidation processes (AOPs) in wastewater treatment to reduce cost, metal contamination, and pH operation limitations. However, they usually encounter low catalytic efficiency because of the difficult single-electron-transfer (SET) pathway during AOPs. Herein, an efficient heterogeneous catalyst for AOPs is realized through the rational regulation of N coordination around Co single-atom (SA) centers in favor of SET. As guided by calculations, low N coordination enables a high density of electronic states at the Fermi energy level of SA Co to facilitate SET activation of peroxomonosulfate (PMS). A special oxide-compounding method is further applied to decrease the N coordination of SA Co on the carbon carriers from common Co1-N3/4 to the desired Co1-N2. Co1-N2 shows a delightful activity for AOP degradation of various organic pollutants with kinetic rate and turnover frequency values up to 0.862 min-1 and 389 h-1, respectively, greatly outperforming those of Co1-N3/4. It is also superior in a wide pH operation range and has strong resistance to environmental disturbances. Detailed mechanistic investigations confirm the generation of singlet oxygen (1O2) instead of common radical O species from the SET between PMS and Co1-N2, corroborating the calculated results and accounting for the enhanced AOP activity.