Abstract. We prove that if T is a tree on n vertices with the maximum value of Graovac-Pisanski index then T is either K_1,3 or K_1,4 or G_7 (a graph obtained from K_1,3 by subdividing every edge once), or P_n or H_n (a graph obtained from double star with two vertices of degree 3 in which the central edge is subdivided sufficiently many times).