In this book, we thoroughly investigated all the possible (406) candidates of half-metallic (HM) antiferromagnet (AFM) with the double Perovskites (DP) structure LaSrBB'O6, La2BB'O6 and Sr2BB'O6, where BB' pairs are any combination of two 3d, 4d and 5d transition elements except for La. Sr could also be replaced by Ca or Ba whenever HM-AFM was found and similar calculation was performed in order to probe more possibilities. In chapter 7, we listed all theoretical prediction results of DP structures LaABB'O6, La2BB'O6 and A2BB'O6(A=Ca, Sr, Ba), in Table 7.1, including our works and others. We tried to give a explaination by GKA (Goodenough-Kanamori-Anderson) rule.