Recently, the first example of Au-Ga clusters is synthesized and characterized, which can be described by the jellium model as a superatom with 8 valence electrons that come from the joint contribution of Au and Ga atoms, opening a whole new field for further research. Here, the structure features and stability of one Ga-doped Au cluster with magic number electrons (6 and 8) are analyzed in detail. Moreover, the valence electron fillings and chemical bonding of them are also further explored. It is found that Au3Ga and Au5Ga clusters present planar configurations, and they have higher stability than that of neighbor clusters. The AIMD simulations show that these two clusters still have a good thermal stability at 500 K. The molecular orbital analyses show that the Au3Ga and Au5Ga have three and one typical delocalization orbital throughout the whole planar spaces, respectively, following the planar σ-aromaticity rule. The ELF and LOL analyses are further performed, and the results are consistent with the molecular orbital analyses. The NICSzz-scan curves confirm that the Au3Ga is more aromatic than the Au5Ga, and the reason is that the former has more delocalized electrons than the latter. Our work opens up aromaticity studies in the Au-Ga clusters.