Cobalt–nitrogen co-doped carbon nanotubes (Co3@NCNT-800) were synthesized via a facile and economical approach to investigate the efficient degradation of organic pollutants in aqueous environments. This material demonstrated high catalytic efficiency in the degradation of carbamazepine (CBZ) in the presence of peroxymonosulfate (PMS). The experimental data revealed that at a neutral pH of 7 and an initial CBZ concentration of 20 mg/L, the application of Co3@NCNT-800 at 0.2 g/L facilitated a degradation rate of 64.7% within 60 min. Mechanistic investigations indicated that the presence of pyridinic nitrogen and cobalt species enhanced the generation of reactive oxygen species. Radical scavenging assays and electron spin resonance spectroscopy confirmed that radical and nonradical pathways contributed to CBZ degradation, with the nonradical mechanism being predominant. This research presents the development of a novel PMS catalyst, synthesized through an efficient and stable method, which provides a cost-effective solution for the remediation of organic contaminants in water.