Ab initio theoretical calculations have been performed to study the reaction of O(2) with Ba(n) (n=2,5) clusters. Our results show that O(2) can easily chemisorb and dissociate on small Ba(n) clusters and there is no obvious energy barrier in the process of the dissociation. The local magnetic moment contributed by oxygen must vanish during the intermediate states before the O(2) dissociation. Correspondingly, local magnetic moment only decreases from 2 mu(B) to about 1 mu(B) if O(2) molecularly adsorbs onto Ba(5) cluster. The electronic structure analysis indicates that the charge transfer from Ba(n) cluster to O(2) as well as the orbital hybridization between the cluster and the oxygen molecule may play a key role in O(2) dissociation.