Recently broadband convergence network technology is emerging as an integrated network of telecommunication, broadcasting and Internet. But there are various threats as side effects against the growth of information technology, and malicious codes such af Internet worms may bring about confusions to upset a national backbone network. In this paper, we survey the traditional spreading models and propose a new worm spreading model on Internet environment. We also analyze the spreading effects due to tile spread period and the response period of Internet worms. The proposed model leads to a better prediction of the scale and speed of worm spreading. It can be applied to high-speed network such as broadband convergence network.