First-principles calculations by the full potential linear muffin-tin orbital (FP-LMTO) method using local spin density approximation (LSDA), taking into account of both spin orbital coupling (SOC) and strong correlation (U) within the framework of spin-polarized density functional theory (DFT), were carried out for the structural, electronic and magnetic properties of a series of double perovskites Ba2CoBO6 (B=Mo, W, Re, Os). Structural optimizations of lattice constants show that all Ba2CoBO6 compounds crystallize in face-centered cubic (FCC) system with space group of (Fm3¯m), in good agreement with the experimental values. The relative stability of ferromagnetic (FM) and antiferromagnetic (AFM) orders is discussed. It is shown that it consistent with experimental results and AFM order is obtained when using LSDA and LSDA+U methods. The magnetic results show that the double perovskites Ba2CoBO6 are AFM through the anti-coupling Co2+ (3d7)↑–O2− (2p)–B6+ (4d/5d)n↓, where n=0, 1 or 2. DFT results show that the Ba2CoBO6 are half-metallic (HM) with energy-gaps in spin-up bands, but if B=Mo, it shows metallic nature in LSDA results, and it established that the U responsible for the AFM-HM in Ba2CoBO6.