IP traceback is a defense method to help a victim to identifying the sources of attacking packets. In this paper, we propose an IP traceback method based on the Chinese Remainder Theorem to require routers to probabilistically mark packets with partial path information when packets traverse routers through the Internet. The routers with the proposed IP traceback method can interoperate seamlessly with legacy routers and be incrementally deployable. The simulation reveals that our method requires fewer numbers of marked packets and takes less time to reconstruct the attacking paths, and has lower false combination rate in comparison with the previous works [10, 13, 15]. Furthermore, by our method, a victim does not need to maintain the network topology while it reconstructs attacking paths.