A subset S of vertices in a graph G is a secure dominating set of G if S is a dominating set of G and, for each vertex u ⁄ ∈ S , there is a vertex v ∈ S such that u v is an edge and ( S ∖ { v } ) ∪ { u } is also a dominating set of G . We show that if G is a maximal outerplane graph of n vertices, then G has a secure dominating set of size at most ⌈ 3 n ∕ 7 ⌉ . Moreover, if a maximal outerplane graph G has no internal triangles, it has a secure dominating set of size at most ⌈ n ∕ 3 ⌉ . Finally, we show that any secure dominating set of a maximal outerplane graph without internal triangles has more than n ∕ 4 vertices.