A highly efficient advanced oxidation process for the degradation of benzoic acid (BA) during activation of peroxomonosulfate (PMS) by nanoscale zero-valent copper (nZVC) in acidic solution is reported. BA degradation was almost completely achieved after 10 min in the nZVC/PMS process at initial pH 3.0. PMS could accelerate the corrosion of nZVC in acidic to release Cu+ which can further activate PMS to produce reactive radicals. Both sulfate radical (SO4-•) and hydroxyl radical (•OH) were considered as the primary reactive oxidant in the nZVC/PMS process with the experiments of methyl (MA) and tert-butyl alcohol quenching. Acidic condition (initial pH ≤ 3.0) facilitated BA degradation and pH is a decisive factor to affect the oxidation capacity in the nZVC/PMS process. Moreover, BA degradation in the nZVC/PMS process followed the pseudo-first-order kinetics, and BA degradation efficiency increased with the increase of the nZVC dosage.