We have investigated the structural, electronic, and magnetic properties of A-site-ordered double-perovskitestructured oxides, AA'3B4O12 (A = Na, Ca, and La) with Mn and V at A' and B sites, respectively, using firstprinciple calculations based on the density functional theory. Our calculation results show that the antiferromagnetic phase is the ground state for all the compounds. By changing the A-site ions from Na+ to Ca2+ and then to La3+, the transfer of charge between Mn and O ions was changed from 1.56 to 1.55 and then to 1.50, and that between the V and O ions changed from 2.01 to 1.95 and then to 1.93, revealing the cause for the unusual site-selective doping effect. Mn 3d electrons dominate the magnetic moment and are localized, with an intense hybridization with O 2p orbitals, which indicates that the magnetic exchange interaction between Mn ions is mediated through O and that the super exchange mechanism will take effect. These materials have a large one-electron bandwidth W, and the ratio of the on-site Coulomb repulsion U to W is less than the critical value (U/W)c, which leads to metallic behavior of AMn3V4O12. This is further evidenced by the large number of free electrons contributed by V at the Fermi surface. These calculations, in combination with the reported experimental data, prove that these double perovskites belong to the rare antiferromagnetic metallic oxides.