The hyper‐Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper‐Wiener index WW(G) is defined as with the summation going over all pairs of vertices in G, and dG(u, v) denotes the distance of the two vertices u and v in the graph G. In this paper, we obtain the second‐minimum hyper‐Wiener indices among all the trees with n vertices and diameter d and characterize the corresponding extremal graphs.