Abstract In this article we have studied the surface structure, rel axation, and oxygen absorbed c(2×2) Cu(001) surface by using ab initio projector augmented wave and Car-Parinello method. It i s concluded that the bond length between oxygen and surface Cu atom is 0.194nm which yields a perpendicular distance of 0.069nm from O to Cu(S). The absor ption of oxygen produces a hybridized band and yields the well localized surface states a t 6.7 eV below E＿F. The calculated work function for this absorbed sur face is 5.29 eV. We also calculate the scanning tunneling microscope images in the Tersoff-Hamann approach and make comparison with available experimental observ ations.