Density functional theory (DFT)-based calculations were carried out to predict the geometry, energy and electronic structures of the small bimetallic Au_mPt_n (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.