A search was made for possible half-metallic (HM) antiferromagnet (AFM) in all the double perovskites structures of Sr2BB'O6 where BB' pairs are any combination of 3d, 4d or 5d transition elements with the exception of La. Sr can also be replaced by Ca or Ba whenever HM-AFM was found and similar calculations were then performed in order to probe further possibilities. It was found that A2MoOsO6, A2TcReO6, A2CrRuO6, where A=Ca, Sr, Ba, are all potential candidates for HM-AFM. The AFM of A2BB'O6 comes from both the superexchange mechanism and the generalized double exchange mechanism via the B(t2g)-O2pπ-B'(t2g) coupling, With the latter also being the origin of their HM. Also considered were the effects of spin-orbit coupling (SOC) and correlation (+U) by introducing +SOC and +U corrections. It is found that the SOC effect has much less influence than the correlation effect on the HM property of the compounds. For A2TcReO6 and A2CrRuO6, after +U, they become nearly Mott-Insulators. In the future, it is hoped that there will be further experimental confirmation for these possible HM-AFM candidates.