Let G = (V, E) be a simple graph. A set D ⊆ V is a dominating set of G if every vertex in V\D is adjacent to at least one vertex in D. D is a 2-dominating set if every vertex in V\D has at least two neighbors in D. A secure dominating set S of a graph G is a dominating set with the property that every vertex u in V\S is adjacent to a vertex v∈S such that (S\{v}) ∪‍ {u} is a dominating set. In this paper, we define and study a new invariant of domination in graphs which is the secure 2-dominating set. A 2-dominating set S is secure 2-dominating if for every vertex u in V\S, ∃v∈(S ∩‍ N(u)) such that (S\{v}) ∪‍ {u} is a 2-dominating set. The secure 2-domination number γ2s(G) is equal to the minimum cardinality of a secure 2-dominating set. First, we establish lower and upper bounds on γ2s (G) of a graph and a triangle-free graph. Then we determine the secure 2-domination number γ2s (G) of paths and cycles. After, we study the complexity of secure 2-domination problem by proving that the determining of the parameters value is NP-complete, also for split and bipartite graphs. Finally, we provide an upper bound of parameter in terms of clique number and independent number for perfect graphs.