Using the first-principles density functional approach, we investigate Ca2FeOsO6, a material of double perovskite structure synthesized recently. According to the calculations, Ca2FeOsO6 is a ferrimagnetic Mott-insulator influenced by the cooperative effect of spin-orbit coupling (SOC) and Coulomb interactions of Fe-3d and Os-5d electrons, as well as the crystal field. When Fe is replaced with Ni, the system exhibits half metallic (HM) states desirable for spintronic applications. In [Ca2Fe1−xNixOsO6]2, HM ferrimagnetism is observed with µtot = 2µB per unit cell for doping rate x = 0.5, whereas HM antiferromagnetism (HMAFM) with nearly zero spin magnetization in the unit cell for x = 1, respectively. It is emphasized that half metallicity is retained even with SOC effect due to the large exchange-splitting between spin-up and spin-down bands close to the Fermi level.