In Graph theory, a dominating set for a graph G is a subset S of its vertices such that every vertex in V-S is adjacent to atleast one vertex in S. The minimum cardinality of a dominating set is called the domination number and is denoted by γ(G). A dominating set S of a graph G is said to be a complementary 3-dominating set of G if for every vertex in S has atleast three neighbors in V-S. The minimum cardinality of a complementary 3-dominating set is the complementary 3-domination number γ_3^' of a graph G. In this paper we determine complementary 3-domination number for some standard graphs and obtain some results concerning this parameter.