The first principle, all-electron, ab initio calculations have been performed for cluster Ga6N6, based on the density functional theory. Ten possible structures and related electronic structures are obtained. For the most stable structure, the mean binding energy of a pair atoms of GaN is 9.748 eV, so the structure may exist. Compared with the results of clusters Ga3N3 and Ga5N5 calculated by other people, however, the cluster Ga6N6 may not be the “magic number” cluster. The Fermi level of cluster Ga6N6 in the most stable structure is partly occupied with EF=-5.2972 eV, which means “metallicity”. The cluster Ga6N6 has no spin magnetic moment. The electron affinity, ionization energy, and transition energies of cluster Ga6N6 are also calculated. This work should be helpful to the complete study of structures and properties of clusters GanNn.