We perform detailed investigations on the electronic and magnetic properties in double perovskites Ba2MOsO6 (M = K, Ca, and Sc), with formal valences of Os7+ (5d(1)), Os6+ (5d(2)), and Os5+ (5d(3)), respectively, using first-principles calculations. To understand the effects of Coulomb interaction (U), spin-orbit coupling (SOC), and magnetic order, we carry out different calculations within density functional theory. It is shown that SOC and U energy not only provide the magneto crystalline anisotropies but also significantly affect the size of the local moments and the magnetic structures in these compounds. The electronic configuration of 5d(1) and 5d(2) of Os in Ba2MOsO6 (M = K and Ca) have the metal-insulator transition (MIT) as the direction of the local moment changes, while the electronic structure of half-filled 5d(3) orbitals of Os in Ba2ScOsO6 is insulator, independent of the local moment direction. Our results indicate that both SOC and U interactions are necessary in enlarging the band gaps and putting these compounds into the MIT correlated insulators.