Dissociative adsorption of O-2 on Cu(001)-(2root2 x root2)-O was shown to induce Cu2O epitaxial islands on the surface. The initial dissociative sticking probability of O-2 on Cu(001)-(2root2 x root2)-O scaled with the total translational energy of incident O-2, suggesting that the interaction potential was highly corrugated. The sticking probability decreased with increasing translational energy of incidence and increased with increasing surface temperature. For lower translational energy of incident O-2 (less than or equal to130 meV), the velocity distribution of the scattered molecules was of nonshifted Maxwellian-type, indicating trapping desorption. The translational temperature of the trapping desorption was lower than the surface temperature and increased linearly with surface temperature, suggesting that there was no barrier for desorption. Neither thermal desorption experiments nor velocity distribution analysis of the trapping desorption showed any evidences of recombination desorption. These results were interpreted as an activated dissociation via a trapping precursor. The activation barrier for dissociation was estimated as 330 meV. The angular distribution of the trapping desorption was fitted well by cos(2) theta, which was in contrast to the expectation of a cosine angular distribution based on the detailed balance arguments. The discrepancy may have been attributable to preferential consumption of the parallel momentum of the trapped O-2 for dissociation and imbalance between adsorbing and desorbing O-2 flux.