With the growing popularity of multicast applications and the recognition of the potential of achievable efficiency gain of traffic grooming, we face the challenge of optimizing the design of WDM networks with multicast traffic grooming. As higher layer electronic ports become the dominant factor of the WDM network cost, it is critical to reduce their number when grooming multicast traffic into high bandwidth light-trees. This paper provides an optimal cost design of WDM networks with multicast traffic grooming. In particular, a light-tree based Integer Linear Programming (ILP) formulation is proposed to minimize the network cost associated with the number of higher layer electronic ports and the number of wavelengths used. Since solving the ILP formulation is time consuming for large networks, we propose a heuristic algorithm, called sub-light-tree saturated grooming (SLTSG), to achieve scalability. This algorithm tries to construct sub-light-trees which can be fully utilized. Simulations are conducted on several networks to compare the design cost and the required number of electronic ports and wavelengths. The results demonstrate significant benefits of using a light-tree based design over a design that only uses lightpaths.