Some fundamental social structures in human population, such as household, dormitory, and colleague, are of significant importance for epidemic spreading. In this paper, a growth model of scale-free network incorporating these local structures is introduced, in which both the node degree and the local structure degree follow a power-law distribution with the exponent depending on the size of the local structure. The existence of the local structures also results in the positive correlation between the nodes degree, which is a particularly key feature of social networks. By means of analysis and simulation, we study the effects of network structure on the SIS（susceptible-infected-susceptible） epidemic dynamics, and obtain the epidemic threshold and the phase diagram of prevalence, indicating that the propagation is coupled by the local infection process within local structure and the global infection process between local structures, both of which are governed by the network features and the transmission mechanism. These results are of scientific significance to the control of infectious diseases.