Electronic structure calculations based on density-functional theory with the generalized gradient approximation for 406 double perovskites have been performed using the accurate full-potential linearized augmented plane wave method. and are found to be candidates of half-metallic (HM) antiferromagnets (AFM) among the 406 ordered double perovskites with all the possible and pairs from all the , , and transition metals have been considered. Furthermore, the HM-AFM state in and survive the full lattice constant and atomic position optimizations which were carried out using the frozen-core full-potential projector-augmented wave method. In addition, the electronic structure calculations have also been performed and the HM-AFM state still remains. Their AFM state is attributed to both the superexchange and generalized double exchange mechanisms via the coupling, and the latter could also be the origin of their HM.