We consider the minimum cost edge installation problem(MCEI) in a graph G=(V, E) with edge weight w(e) ≥ 0, e ∈ E. We are given a vertex s ∈ V designated as a sink, an edge capacity λ > 0, and a source set S ⊆ V with demand q(v) ∈ [0, λ], v ∈ S. For each edge e ∈ E, we are allowed to install an integer number h(e) of copies of e. MCEI asks to send demand q(v) from each source v ∈ s along a single path P_v to the sink s without splitting the demand of any source v ∈ S. For each edge e ∈ E, a set of such paths can pass through a single copy of e in G as long as the total demand along the paths does not exceed the edge capacity λ. The objective is to find a set P = {P_v | v ∈ S} of paths of G that minimizes the installing cost ∑_e∈E h(e) w(e). In this paper, we propose a (15/8+_ρST)-approximation algorithm to MCEI, where _ρST is any approximation ratio achievable for the Steiner tree problem.