A complex magnetic order of the multiferroic compound Co3TeO6 has been revealed by neutron powder diffraction studies on ceramics and crushed single crystals. The compound adopts a monoclinic structure (s.g. C2/c) in the studied temperature range 2-300 K but exhibits successive antiferromagnetic transitions at low temperature. Incommensurate antiferromagnetic order with the propagation vector k(1) = (0, 0.485, 0.055) sets in at 26 K. A transition to a second antiferromagnetic structure with k(2) = (0, 0, 0) takes place at 21.1 K. Moreover, a transition to a commensurate antiferromagnetic structure with k(3) = (0, 0.5, 0.25) occurs at 17.4 K. The magnetic structures have been determined by neutron powder diffraction using group theory analysis as a preliminary tool. Different coordinations of the Co2+ ions involved in the low-symmetry C2/c structure of Co3TeO6 render the exchange-interaction network very complex by itself. The observed magnetic phase transformations are interpreted as an evidence of competing magnetic interactions. The temperature dependent changes in the magnetic structure, derived from refinements of high-resolution neutron data, are discussed and possible mechanisms connected with the spin reorientations are described. (C) 2011 Elsevier Ltd. All rights reserved.