The sum-connectivity index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. The graphs called two-trees are defined by recursion. The smallest two-tree is the complete graph on two vertices. A two-tree on [Formula: see text] vertices (where [Formula: see text]) is obtained by adding a new vertex adjacent to the two end vertices of one edge in a two-tree on [Formula: see text] vertices. In this paper, the sharp lower bound on the sum-connectivity index of two-trees is presented, and the two-trees with the minimum and the second minimum sum-connectivity, respectively, are determined.