The adsorption of Au on clean Si(001) surface is investigated by the local density approximation using first-principles pseudopotentials. We found that the adsorption energy of Au on ideal Si(001)-(1×1) surface is lower than that on reconstructed Si(001)-(2×1) surface, suggesting that adsorbed Au atoms chemically react with the surface Si atoms and break Si-Si dimer bonds of the substrate. Furthermore, the intermixing of Au and Si is also considered and the calculation suggests that intermixing will not take place at low temperature. But due to the small energy barrier for Au atoms to diffuse into Si substrate, we can conclude that the Au-Si alloy is easily formed at relatively high temperature. This result should be one of the reasons of the lack of consensus on the issue of intermixing of Au and Si.