Density functional theory (DFT)-based calculations were carried out to predict the geometry, energy and electronic structures of the small bimetallic AumPtn (2 ≤m + n≤ 4) clusters deposited on a single-wall (5,5)-carbon nanotube (CNT). The chemical reactivity of these supported bimetallic clusters towards O2 reduction reaction was also considered. The calculations indicate that Au atoms tend to avoid the CNT atoms, whereas the opposite occurs for Pt atoms, a behavior which can be rationalized through analyses of the density of states plots. Compared to isolated clusters, the supported counterparts are found to have significant superiority in catalytic activity towards O2 reduction. The adsorption configuration and identity of the metal (Au or Pt) exposed to the O2 molecule adsorption are the dominant factors in determining the catalytic activity of the supported particles. Most notably, high catalytic activity of the supported clusters is associated with a drastic decrease in adsorption energy of the O2 molecule.