The first-principles technique is employed to determine the adsorption system of the CO monolayer on Cu(100) surface under the coverages of 1.00 ML, 0.50 ML and 0.25 ML. The calculation shows that the CO dimer is not stable enough. The atomic structures of CO monolayer on virtual Cu(100) surface and in the adsorption system on Cu(100) surface are proposed. In the CO/Cu(100) adsorption system, under the coverage of 1.00 ML the top and bridge sites are both stable, but the hollow site is not stable enough; under the coverages of 0.50 and 0.25 ML three adsorption sites are all stable. A comparison of the structure of the CO monolayer between before and after adsorption on Cu(100) surfrace shows that the interaction between the CO molecule and Cu(100) is clearly stronger than that between the CO monolayers.