  The terminal Wiener index of a tree is the sum of distances for all pairs of
pendent vertices, which recently arises in the study of phylogenetic tree
reconstruction and the neighborhood of trees. This paper presents a sharp upper
and lower bounds for the terminal Wiener index in terms of its order and
diameter and characterizes all extremal trees which attain these bounds. In
addition, we investigate the properties of extremal trees which attain the
maximum terminal Wiener index among all trees of order $n$ with fixed maximum
degree.
