The absorption behavior of copper atoms on the armchair （5,5） single wall carbon nanotube is investigated by the density functional theory. It is shown that the absorption on the outside nanotube is energetically preferred to that on the inside nanotube, Morever, the adsorbed copper atom on the top of carbon is more stable than that on the other outside sites. At the same time, the characteristic of the forming bond on the top of carbon between copper and SWNT is detailed. The absorption behavior belongs to chemical absorption, and based on the analysis of frontier orbital, it is shown that the new σ bond is mainly due to the interaction of 4s valence state of copper and coupling σ-π bond of SWNT. Furthermore, the calculated electron densities of two representative adsorption positions show that electron clouds overlap more on the top of carbon adsorbed copper atom， which further confirms that copper and carbon atoms can form chemical bond in a sense.