We have performed total energy calculations on the structural and adsorption properties of Cu(100) c(2×2)-N surface by using DFT PAW method. It is concluded that nitrogen adsorbed on a four-fold coordinated site with a perpendicular distance of 0.2? from the surface Cu layer. The shortest Cu-N bond length is calculated to be 1.83?. Geometry optimization calculation excludes the possibilities of adsorbate induced reconstruction mode suggested by Driver and Woodruff and the atop model. The simulated work function for this absorbate-substrate system is 4.65 eV which is quite close to that on the clean Cu(100) surface. The total energy calculations showed that the average adsorption energy per nitrogen atom in the case of Cu(100) c(2×2)-N is about 4.92 eV with respect to a solitude N atom. The absorption of nitrogen on the Cu(100) surface yields the hybridization between surface Cu and N atoms, and generates the localized surface states at -1.0 eV relative to Fermi energy EF. The present study provides a strong criterion to account for the argument on the scanning tunneling microscopy(STM) images from different research groups.