Applying the SIS (susceptible-infected-susceptible) model, we study the epidemic spreading on the web of human sexual contacts. When only heterosexual contacts are considered, the web is a bipartite scale-free network. By using the rate equation approach, we analyze the relation between epidemic threshold and infection rates of female-to-male and male-to-female. We find that the ratio of infected female density to infected male density is determined by the topology of the network and the proportion between infection rates of females and males. This demonstrates the importance of the topology of network. Finally, we present numerical simulation results that support the analytic results.