Let G be a simple graph with vertex set V = V(G) = {v1, v2,…, vn} and edge set E = E(G). For vi ∈ V(G), by di = di(G) we denote the degree (number of neighbors) of the vertex vi. The second Zagreb index is defined as M2(G) = ∑ vivj∈E(G) didj. In this paper, we study the minimal and maximal second Zagreb index of trees with fixed diameter.