The advanced oxidation process (AOP) based on SO4- radicals draws an increasing interest in water and wastewater treatment. Producing SO4- radicals from the activation of peroxymonosulfate (PMS) by transition metal ions or oxides may be problematic due to high operational cost and potential secondary pollution caused by metal leaching. To address this challenge, the present study reports the efficient production of SO4- radicals through visible-light-driven photocatalytic activation (VL-PCA) of PMS by using Cu2(OH)PO4 single crystal for enhanced degradation of a typical recalcitrant organic pollutant, i.e., 2,4-dichlorophenol (2,4-DCP). It took only 7 min to achieve almost 100% removal of 2,4-DCP in the Cu2(OH)PO4/PMS system under visible-light irradiation and pH-neutral condition. The 2,4-DCP degradation was positively correlated to the amount of Cu2(OH)PO4 and PMS. Both OH and SO4- radicals were responsible for enhanced degradation performance, indicated by radical scavenger experiments and electron spin resonance (ESR) measurements. The Cu2(OH)PO4 single crystal exhibited good cyclic stability and negligible metal leaching. According to density functional theory (DFT) calculations, the visible-light-driven transformation of two copper states between trigonal bipyramidal sites and octahedral sites in the crystal structure of Cu2(OH)PO4 facilitates the generation of OH and SO4- radicals from the activation of PMS and cleavage of O-O bonds. This study provides the proof-in-concept demonstration of activation of PMS driven by visible light, making the SO4- radicals-based AOPs much easier, more economical and more sustainable in engineering applications for water and wastewater treatment.