Let be a graph. A set of a graph is called a total dominating set if the induced subgraph has no isolated vertices. The total domination number of G is the minimum cardinality of a total dominating set of G . A total dominating set D is said to be a complete cototal dominating set if the induced subgraph has no isolated vertices. The complete cototal domination number of G is the minimum cardinality of a complete cototal dominating set of G . In this paper, we initiate the study of complete cototal domination in graphs and present bounds and some exact values for . Also its relationship with other domination parameters are established and related two open problems are explored.