An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyclic (CODC) if the cyclic group of order is a subgroup of the automorphism group of G. In this paper, we introduce a general orthogonal labelling for CODC of circulant graphs and construct CODC by certain classes of graphs such as complete bipartite graph, the union of the co-cycles graph with a star, the center vertex of which, belongs to the co-cycles graph and graphs that are connected by a one vertex.