The Wiener index W (G) of a connected graph G is the sum of distances of all pairs of vertices in G. In this paper, we show that for any even positive integer k , and n ≥ k + 1 , if G is a k -connected graph of order n , then W (G) ≤ W (C n k 2 ) , where G k is the k th power of a graph G. This partially answers an old problem of Gutman and Zhang.