Carbon nanotubes have important applications in gas adsorption. Therefore the study of their properties for this application is very important. In this study the Density Functional Theory (DFT) and Hartree-Fock (HF) methods were used to investigate the adsorption of oxygen molecules on the surface of (5, 0) and (4, 4) carbon nanotubes. The electronic structure, and dipole moment of both oxygen and carbon nuclei are thoroughly studied. The computational results indicate that rich adsorption patterns may result from the interaction of oxygen with the carbon nano-tubes.; sometimes C-O bounds are formed via breaking C-C bounds and sometimes a carbon atom in the nano-tube is replaced with a oxygen atom. Sometimes oxygen atoms are attracted to a C-C bound. In summary, the optimized adsorption rates are calculated. Gaussian 98 software has been used to carry out quantum chemistry calculations.