Using first-principle calculations, the structural, electronic, and magnetic properties of the Ca 2 FeMoO 6 double perovskite compound is investigated. Different spin-ordering: ferrimagnetic (FiM), ferromagnetic (FM), and anti-ferromagnetic (AFM1 and AFM2) using the generalized gradient approximation (GGA) and GGA + U (Hubbard Coulomb onsite correction) are evaluated to determine the theoretical ground state. The value of the Hubbard Coulomb U parameter is varied from 1 to 4 eV. The ground state is found to be a FM spin-ordering within the GGA approach and FiM spin-ordering within the GGA + U approach (where U ≥ 3 eV) which is the experimental preferred configuration. We obtain the FiM spin-ordered half semiconducting state within the GGA + U approach for the Ca 2 FeMoO 6 compound. Within the GGA + U (where U ≥ 3 eV) approach, the FM phase maintains a half-metallic character with a net magnetic moment of 4 0 μ B , whereas the FiM phase have a spin gapless semiconducting (SGS) behavior at U = 3 eV, and an insulating character at U = 4 eV, with a net magnetic moment of 4 0 μ B . The main features found in the density of states profile show that the hybridization of the Fe and Mo d orbitals play an important role in determining the electronic and magnetic character of this compound.