A subset S of a graph G is called a dominating set of G if every vertex in $V-S$ is adjacent to at least one vertex in S. The domination number $\gamma(G)$ is the minimal cardinality of a dominating set. A dominating set S in a graph G is said to be a complementary 3-dominating set of G if any vertex in S has at least three neighbours in $V-S$. The complementary 3-domination number $\gamma_3'(G)$ of a graph G is the minimum cardinality of a complementary 3-dominating set. We determine complementary 3-domination number for some special graphs and proved some theorem in cubic graphs.