The propagation and evolution model of botnet is the most common method to study the spreading features of bots, but current botnets' propagation and evolution models limited to describe active spread process based on worms, don't consider the passive spread process similar to """"plugged Trojan-horse into webpage"""", so these models can not exactly describe how the bots spread on the Internet. In this paper, a new botnet propagation and evolution model (WT-SIR) was proposed. This model carefully considers about the real situation of the Internet, especially probability of bots' status transformed from infected and immune to susceptible. Simulation result shows that the WT-SIR model more exactly satisfies the practical propagation laws and infection characteristics of bots on Internet.