Chemical functionalization of carbon nanotubes with Stone-Wales ( SW) defects by carboxyl ( COOH) groups is investigated by density functional calculations. Due to the localized donor states induced by the SW defect, the binding of the COOH group with the defective carbon nanotube is stronger than that with the perfect one. A quasi-tetrahedral bonding configuration of carbon atoms, indicating sp(3) hybrid bonding, is formed in the adsorption site. The charge distribution analysis shows that, in comparison with benzoic acid, the localized or delocalized pi states on the nanotube would affect the polarities of chemical bonds of the COOH group without losing the acidity. Furthermore, it is found that the double-adsorption system ( two COOH groups are respectively adsorbed on two individual carbon atoms of the SW defect) is more energetically favorable than the monoadsorption one. The adsorption of COOH groups leads to a significant change of the electronic states around the Fermi level, which is advantageous for the electrical conductivity. The functionalization by introducing functional groups on the topological defects provides a pathway for applications of carbon nanotubes in chemical sensors and nanobioelectronics.