The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate a chemical compound’s molecular graph with experimentally gathered data regarding the compound’s characteristics. In [M. Fischermann, A. Hoffmann, D. Rautenbach, L.A. Székely, L. Volkmann, Wiener index versus maximum degree in trees, Discrete Appl. Math. 122 (1–3) (2002) 127–137], the tree that minimizes the Wiener index among trees of given maximal degree is studied. We characterize trees that achieve the maximum and minimum Wiener index, given the number of vertices and the degree sequence.