First-principle density functional theory is used for studying the anion gold clusters doped with magnesium atom. By performing geometry optimizations, the equilibrium geometries, relative stabilities, and electronic and magnetic properties of [AunMg](-) (n = 1-8) clusters have been investigated systematically in comparison with pure gold clusters. The results show that doping with a single Mg atom dramatically affects the geometries of the ground-state Au-n+1(-) clusters for n = 2-7. Here, the relative stabilities are investigated in terms of the calculated fragmentation energies, second-order difference of energies, and highest occupied-lowest unoccupied molecular orbital energy gaps, manifesting that the ground-state [AunMg](-) and Au-n+1(-) clusters with odd-number gold atoms have a higher relative stability. In particular, it should be noted that the [Au3Mg](-) cluster has the most enhanced chemical stability. The natural population analysis reveals that the charges in [AunMg](-)(n = 2-8) clusters transfer from the Mg atom to the Au frames. In addition, the total magnetic moments of [AunMg](-) clusters exhibit an odd even oscillation as a function of cluster size, and the magnetic effects mainly come from the Au atoms.