Summary: Given a complete graph \(G=(V,E)\), with nonnegative edge costs, two subsets \(R\subset V\) and \(R'\subset R\), a partition \(\mathcal{R}=\{R_1, R_2,\dots,R_k\}\) of \(R\), \(R_i\cap R_j=\emptyset\), \(i\neq j\) and \(\mathcal{R}'=\{R_1', R_2',\dots,R_k'\}\) of \(R'\), \(R_i'\subset R_i\), a clustered Steiner tree is a tree \(T\) of \(G\) that spans all vertices in \(R\) such that \(T\) can be cut into \(k\) subtrees \(T_i\) by removing \(k-1\) edges and each subtree \(T_i\) spans all vertices in \(R_i\), \(1\leq i\leq k\). The cost of a clustered Steiner tree is defined to be the sum of the costs of all its edges. A clustered selected-internal Steiner tree of \(G\) is a clustered Steiner tree for \(R\) if all vertices in \(R_i^\prime\) are internal vertices of \(T_i\). The clustered selected-internal Steiner tree problem is concerned with the determination of a clustered selected-internal Steiner tree \(T\) for \(R\) and \(R'\) in \(G\) with minimum cost. In this paper, we present the first known approximation algorithm with performance ratio \((\rho+4)\) for the clustered selected-internal Steiner tree problem, where \(\rho\) is the best-known performance ratio for the Steiner tree problem.