In this paper, we investigate the epidemic spreading for the SIR model in weighted scale-free networks with the nonlinear infectivity and weighted transmission rate. Concretely, we introduce the infectivity exponent α and the weight exponent β into the epidemic system, then examine the impact of α and β on the epidemic spreading. We show that one can adjust the values of α and β to rebuild a nonzero finite epidemic threshold. Furthermore, we also find the infectivity exponent α has a stronger effect not only on the epidemic threshold, but also on the epidemic prevalence. In addition, it is also interesting to see that the absence of the epidemic threshold appears not very dejected, since the prevalence grows much more slowly as the transmission rate λ increases.