A vertex $u$ in graph $G$ dominates itself and all its neighbers and also $u$ $k$-dominates itself and all vertices by distance within $k$ from $u$. A set $D\subseteq V(G)$ $k$-dominates $G$ if each vertex in $G$ is $k$-dominated by at least one vertex in $D$ and is called a distance $k$-dominating set of G. The minimum cardinality among all distance $k$-dominating sets of $G$ is called the distance $k$-domination number of $G$. We will give an upper bound for distance $k$-domination number of connected bipartite graphs.
