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

An upper bound on the Wiener Index of a k-connected graph