  The Wiener index of a connected graph is the summation of all distances
between unordered pairs of vertices of the graph. In this paper, we give an
upper bound on the Wiener index of a $k$-connected graph $G$ of order $n$ for
integers $n-1>k \ge 1$:
  \[W(G) \le \frac{1}{4} n \lfloor \frac{n+k-2}{k} \rfloor (2n+k-2-k\lfloor
\frac{n+k-2}{k} \rfloor).\] Moreover, we show that this upper bound is sharp
when $k \ge 2$ is even, and can be obtained by the Wiener index of Harary graph
$H_{k,n}$.
