The growth of the Internet technology enables us to use network applications for streaming audio and video. Especially, real-time streaming services using peer-to-peer (P2P) technology are currently emerging. An important issue on P2P streaming is how to construct a logical network (overlay network) on a physical network (IP network). In this paper, we propose an initial peer configuration algorithm for a multi-streaming peer-to-peer network. The proposed algorithm is based on a mesh-pull approach where any node has multiple parent and child nodes as neighboring nodes, and content transmitted between these neighboring nodes depends on their parent-child relationships. Our simulation experiments show that the proposed algorithm improves the number of joining node and traffic load.