The electronic structure of the CoV2O6 magnetic oxide is investigated using first principle density functional theory calculations with the full potential linearized augmented plane wave method. The spin-orbit coupling (SOC) and the GGA + U functional are included in order to determine the orbital magnetic moment (OMM) for the monoclinic C2/m (or alpha phase) structure where, experimentally, the ground state is found insulating with a large magnetic moment perpendicular to the chains direction in an antiferromagnetic configuration. It is exhibited, that the perturbation approach of the SOC gives only small OMM values but large ones can be obtained when special initial charge densities are used. An OMM as large as 1.5 mu(B) in the direction of the octahedron axis perpendicular to the chains is obtained in agreement with the experiment. The electronic structure analysis shows that this large OMM results from the occurrence of a (zxyz) hybridized state. (C) 2014 Elsevier B.V. All rights reserved.