Boyh diffusion and epidemic are well studied in the stochastic systems and complex networks,respetively.Here we combine these two fields and study epidemic diffusion in complex networks.Instead of studying the threshold of infection,which was focused on in previous works,we focus on the diffusion.behaviour.We find that the epidemic diffusion in a complex network is an anomalous superdiffusion with varyingg diffusion exponext γand that γ is influenced seriously by the network structure,such as the clustering coefficient and the degree distribution.Numerical simulations have confirmed the theoretical predictions.