In order to address some deployment problems of IP multicast, the notion of Multicast Service Overlay Network (MSON) is proposed. How to construct MSON satisfying user’s demand efficiently under the situation of limited resources is a hot issue. In this paper we analyze a mathematics model of MSON construction. Under the objective of finding a virtual topology on top of physical network fulfilling all restrictions, and minimizing the cost of construction while keeping residual physical network the most balanced, an Integer Linear Programming model of the construction problem is depicted. In order to solve the problem efficiently, we propose a heuristics algorithm named BLMH. The efficiency of BLMH is evaluated by emulation experiment according to congestion link number under several scenarios.