A first principles plane-wave method was utilized to investigate the band structure, lattice parameters and total energy for AuCd B2, γ2’ and ζ2’ structures. The results are in good agreement with experimental results. We have found that the band structures for three structures are very similar: steep profile above Fermi level, and flat blow the Fermi level. In the three structures, γ2’ phase holds the lowest energy, and the order of stability is γ2’>ζ2’> B2. AuCd γ2’ structure changes its lattice parameters according to a common principle that is lattice parameter a diminishes and b and c become larger. This result consists with the experimental result.