In this paper we consider a model with demographics for sexually transmitted diseases (STDs) spread on scale-free networks. We derive the epidemic threshold, which is depend on the birth rate, the natural death rate and other parameters. The absence of a threshold in infinite scale-free network is proved. For a hard cut off scale-free network, we also analyze the stability of disease-free equilibrium and the persistence of STDs infection. Two immunization schemes, proportional scheme and targeted vaccination, are studied and compared. We find that targeted strategy is more effective on scale-free networks.