The electronic structure and magnetic properties of Fe3O4 have been studied by density functional method in the frame of local density approximation. Gradually reducing the symmetry has been used to establish different cation distribution of the studied compound. This symmetry cracking introduces some evidences for the half-metallicity of Fe3O4. Different experimental distributions, of cations Fe+2 and Fe+3 between tetrahedral A-site and octahedral B-site for spinel structure, have been calculated. The magnetic anisotropy through the spin-orbit coupling (SOC) has been calculated, where the results revealed a pronounced agreement with the experimental results. These SOC calculations have been conducted for different directions of the magnetization, where semiconductor and metallic behavior for majority and minority channels, respectively, are still found respectively. As for Fe in B-site, the spin orbital angular momentum coupling component of the magnetic momentis considerably larger than that for Fe in A-site. This urges some states of Fe-3d electrons on B-siteto have higher energy states than the Fermi energy.