Abstract: The problem of epidemic spreading has always been concerned by many scientists all over the world.However，there are no studies in the field of weighted local-world network.Since a lot of the real-world networks are weighted，the virus spreading in weighted local-world complex networks is studied in this paper.With the SI model of virus spreading being adopted and the virus spreading speed between any two nodes being positive correlation with the corresponding weight between them，the effect of different weight distributions on the spreading behavior in three weighted evolving networks is investigated.Study shows that scale-free and Weighted local-world properties of weighted local-world network both have an great effect on the Epidemic spreading.As the weighted local-world model can well reflex the real world，these research has board practical background.