We calculated electronic structures of double perovskite structures of A2MoOsO6 and A2TcReO6 (A = Si, Ge, Sn, and Pb) based on the density functional theory which was carried out with a full structural optimization using generalized gradient approximation and taking into account the correlation effect (GGA + U). In GGA calculation, Pb2TcReO6 shows a half-metallic antiferromagnet (HM-AFM) characteristic, whereas Sn2MoOsO6, Pb2MoOsO6, and Sn2TcReO6 are nearly HM-AFMs. With GGA + U calculation, Sn2MoOsO6 and Pb2MoOsO6 become stable HM-AFM, but Sn2TcReO6 and Pb2TcReO6 changes HM-AFM into an antiferromagnetic insulator. The p–d hybridization between B(B′)d-Op and double exchange interaction is the mean reason to result in the half-metallic and compensated ferrimagnetic phase.