Density functional theory and slab models are employed to study NO molecule adsorption and reaction on clean and atomic oxygen precovered Au(111) surfaces. While clean Au(111) surface is catalytically inert and can only weakly adsorb NO, an atomic oxygen precovered Au(111) surface is found to be very active to NO. On the clean surface, NO prefers to bond at the onefold on-top surface site with a tilted geometry. On 0.33 ML (monolayer) oxygen precovered surface NO reacts with chemisorbed oxygen to form chemisorbed NO(2) by conquering a small energy barrier about 0.18 eV, and the desorption energy of NO(2) is 0.64 eV. On 1.0 ML oxygen coverage surface, no barrier is found while NO reacts with precovered oxygen. The desorption energy of NO(2) is 0.03 eV. The desorption of NO(2) is the rate determining step on both surfaces and the overall reaction barriers are 0.64 and 0.03 eV, respectively. The activation energies depend on the initial coverage of oxygen, which compare favorably with experiments on Au surface with different oxygen coverages.