The adsorption behaviour of a single O atom on Aun(q) clusters (n = 1-8, q = 0, ±1) was systematically investigated by DFT calculations. Both hybrid and pure GGA functionals (B3LYP and PBE) were used to provide reliable conclusions. The most stable structures of AunO(q) clusters were obtained by using global optimizations with a genetic algorithm. Cationic clusters tend to become three-dimensional for large clusters, as for Au8O(+). The binding of O in AunO(q) clusters is quite strong, especially in the anionic clusters. The O atom can be bound to one, two, or three Au atoms, obtaining nearly one electron from gold atoms. Similarities have been found between AunO(q) and Aun+1(q) in terms of geometric structures and binding energies. Frontier molecular orbitals and the distribution of unpaired spin density on the O atom were discussed, both of which have a close relationship with the activity of the clusters.