The chemisorption of one monolayer of Au atoms on an ideal Si(001) surface is studied by using the self-consistent tight binding linear muffin-tin orbital method. Energies of the adsorption system of a Au atom on different sites are calculated. It is found that the most stable position is A site (top site) for the adsorbed Au atoms above the Si(001)surface. It is possible for the adsorbed Au atoms to sit below the Si(001) surface at the B1 site(bridge site), resulting in a Au-Si mixed layer. This is in agreement with the experiment results. The layer projected density of states is calculated and compared with that of the clean surface. The charge transfer is also investigated.