  A vertex-colored graph $G$ is rainbow vertex-connected if any pair of
distinct vertices are connected by a path whose internal vertices have distinct
colors. The rainbow vertex-connection number of $G$, denoted by $rvc(G)$, is
the minimum number of colors that are needed to make $G$ rainbow
vertex-connected. In this paper we give a Nordhaus-Gaddum-type result of the
rainbow vertex-connection number. We prove that when $G$ and $\bar{G}$ are both
connected, then $2\leq rvc(G)+rvc(\bar{G})\leq n-1$. Examples are given to show
that both the upper bound and the lower bound are best possible for all $n\geq
5$.
