Elemental mercury (Hg) adsorptions on small neutral, cationic and anionic gold clusters, Auqn (n=1—6, q=0, +1, -1), are systematically investigated by using the density functional theory(DFT) in the generalized gradient approximation. The result shows that the frontier molecular orbital theory (FMOT) is useful for predicting the favorable binding configurations of Hg adsorbed on neutral and charged Aun clusters. Most of the lowest energy AunHg complexes can be successfully predicted. The size and the charge state of the clusters have strong influence on the adsorption of Hg on gold clusters. The adsorption energy on the neutral clusters reaches a local maximum at n=4, which is about 0.661eV. The adsorption energies for cationic clusters decrease with cluster size increasing, although there is a local peak at n=5. Similarly, for anionic clusters, the adsorption energies decrease with cluster size, except for n=3. The adsorption energies on the cationic clusters are generally stronger than those on the neutral and anionic clusters. For the lowest energy AunHg complexes, an approximate linear correlation between the adsorption energy and the Mulliken charge on adsorbed Hg is found. The more the charges transfer to the cluster, the higher the adsorption energy is.