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 Pv 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={Pv| 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.