  An outer-connected dominating set for an arbitrary graph $G$ is a set
$\tilde{D} \subseteq V$ such that $\tilde{D}$ is a dominating set and the
induced subgraph $G [V \setminus \tilde{D}]$ be connected. In this paper, we
focus on the outer-connected domination number of the product of graphs. We
investigate the existence of outer-connected dominating set in lexicographic
product and Corona of two arbitrary graphs, and we present upper bounds for
outer-connected domination number in lexicographic and Cartesian product of
graphs. Also, we establish an equivalent form of the Vizing's conjecture for
outer-connected domination number in lexicographic and Cartesian product as
$\tilde{\gamma_c}(G \circ K)\tilde{\gamma_c}(H \circ K) \leq
\tilde{\gamma_c}(G\Box H)\circ K$. Furthermore, we study the outer-connected
domination number of the direct product of finitely many complete graphs.
