Different configurations of a single nitrogen atom adsorbed at different sites on the sidewall of single-walled carbon nanotubes (SWNT's) are studied through first-principles calculations. It is found that the outer surface of the tube wall is reactive to the nitrogen atom, and a nitrogen atom can be chemically adsorbed on it forming an exohedral complex with a binding energy of; 3.86eV for a (5,5) SWNT. Although the inner surface of the tube wall is less reactive than the outer surface, a nitrogen atom can still be adsorbed on the inner wall of the (5,5) tube forming an endohedral complex with the binding energy on the order of ～1.78eV. The local structure of the SWNT around the adsorption sites is substantially changed. From studying the binding energies of a nitrogen atom adsorbed on different armchair tubes (n, n) with n ranging from 5 to 16, it is found that the binding energy for exohedral adsorption decreases significantly with increasing radius (or increasing n) of the tube, while for endohedral adsorption the binding energy varies slightly. The influence of endohedral adsorption of a single nitrogen atom on the local density of states of a (5,5) SWNT is also discussed.