The generalized ABC index of a graph G, denoted by ABC?, is defined as the sum of the terms [(d(v) + d(u)-2)/d(v)d(u)]? over all pairs of adjacent vertices, where d(u) is the degree of the vertex u and ? is a real number. In this paper, we prove that for ? ?-1, the balanced double broom is the unique tree that minimizes AB?C among trees of order n with diameter d, and trees of order n with k pendent vertices.