In this study, a new hollow nanotube material, 30% Co–CHNTs was prepared by the impregnation–chemical reduction–calcination method. This material can be used as a peroxymonosulfate (PMS) activator to catalyse the degradation of sulfamethoxazole (SMX). The best reaction conditions that correspond to the degradation rate of SMX, up to 97.5%, are as follows: the concentration of SMX is 10 mg L−1, the amount of catalyst is 0.20 g L−1, the dosage is 1.625 mM, and the solution pH is 6.00. X-ray photoelectron spectroscopy (XPS) and inductively coupled plasma optical emission spectrometry (ICP-OES) show that the calcined composites mainly stimulate an increase in the content of bivalent cobalt in PMS and reduce the leaching of cobalt ions after the reaction. Additionally, the 30% Co–CHNTs + PMS reaction system exhibits a reasonable SMX degradation rate in a natural organic matter solution and excellent stability after three repeated experiments. Furthermore, the possible degradation mechanism in the 30% Co–CHNTs + PMS reaction system was analysed through electron paramagnetic resonance (EPR) and free-radical capture experiments, and it was observed that the non-radical degradation of 1O2 plays a leading role in SMX degradation. Finally, according to the nine degradation intermediates detected by liquid chromatography-mass spectrometry (LC–MS), four possible SMX degradation routes were proposed. This study proved that a 30% Co–CHNTs heterogeneous catalyst is easily prepared, inexpensive, and environmentally friendly and has potential application in antibiotic wastewater treatment.