In this work, first-principles density functional theory (DFT) is used to predict oxygen adsorption on two types of hybrid carbon and boron-nitride nanotubes (CBNNTs), zigzag (8,0), and armchair (6,6). Although the chemisorption of O2 on CBNNT(6,6) is calculated to be a thermodynamically unfavorable process, the binding of O2 on CBNNT(8,0) is found to be an exothermic process and can form both chemisorbed and physisorbed complexes. The CBNNT(8,0) has very different O2 adsorption properties compared with pristine carbon nanotubes (CNTs) and boron-nitride nanotube (BNNTs). For example, O2 chemisorption is significantly enhanced on CBNNTs, and O2 physisorption complexes also show stronger binding, as compared to pristine CNTs or BNNTs. Furthermore, it is found that the O2 adsorption is able to increase the conductivity of CBNNTs. Overall, these properties suggest that the CBNNT hybrid nanotubes may be useful as a gas sensor or as a catalyst for the oxygen reduction reaction.