Display omitted •CoM/TNTs showed high ACE degradation efficiency after PMS activation.•Efficient PMS activation was due to the synergic effect of Co(OH)2 and TNTs.•TNTs with abundant surface –OH facilitated formation of CoOH+.•PES analysis well explained the higher feasibility of Co(OH)+ on PMS activation.•ACE atoms with high Fukui index are active sites for electrophilic attack. Pharmaceuticals and personal care products (PPCPs) are of great concern due to their increasing health effects, so advanced treatment technologies for PPCPs removal are urgently needed. In this study, titanate nanotubes decorated Co(OH)2 hollow microsphere (CoM/TNTs) composites were synthesized by a two-step solvothermal method, and used to activate peroxymonosulfate (PMS) through heterogenous catalysis for acetaminophen (ACE) degradation in water. The optimum material (CoM/TNTs0.5) activated PMS system exhibited high ACE removal efficiency and quick kinetic, as 93.0% ACE was degraded even within 10 min. The two components in CoM/TNTs showed a synergetic effect on PMS activation for radicals production: Co(OH)+ from CoM was the primary active species to active PMS, while TNTs could offer abundant –OH groups for Co(OH)+ formation. Density functional theory (DFT) calculation further interpreted the mechanism of Co(OH)+ for PMS activation by means of reaction potential energy surface (PES) analysis. Both the scavenger quenching tests and electron paramagnetic resonance analysis revealed that the sulfate radical (SO4-·) played a dominant role in ACE degradation. Moreover, DFT calculation also suggested that the ACE atoms with high Fukui index (f-) represented the active sites for electrophilic attack by SO4-·. The toxicity analysis based on quantitative structure-activity relationship (QSAR) verified the reduced toxicity of transformation products. Furthermore, CoM/TNTs also had good reusability and stability over five cycles. This work provides deep insights into the reaction mechanisms of radical production and organics attack in cobalt-based PMS activation system.