We have investigated the HO2 adsorption and acid dissociation process on the surface of (H2O)20 and (H2O)21 clusters by using quantum-chemistry calculations. Our results show that the radical forms a stable hydrogen-bond complex on the cluster. The HO2 acid dissociation is more favorable in the case of the (H2O)21 cluster, for which the inner water molecule plays a crucial role. In fact, acid dissociation of HO2 is found to occur in two steps. The first step involves H2O autoionization in the cluster, and the second one involves the proton transfer from the HO2 radical to the hydroxide anion. The presence of the HO2 radicals on the surface of the cluster facilitates water autoionization in the cluster.