Voluntary vaccination reflects how individuals weigh the risk of infection and the cost of vaccination against the spread of vaccine-preventable diseases, such as smallpox and measles. In a homogeneously mixing population, the infection risk of an individual depends largely on the proportion of vaccinated individuals due to the effects of herd immunity. While in a structured population, the infection risk can also be affected by the structure of individuals' social network. In this paper, we focus on studying individuals' self-organizing behaviors under the circumstance of voluntary vaccination in different types of social networks. Specifically, we assume that each individual together with his/her neighbors forms a local well-mixed environment, where individuals meet equally often as long as they have a common neighbor. We carry out simulations on four types of locally-mixed social networks to investigate the network effects on voluntary vaccination. Furthermore, we also evaluate individuals' vaccinating decisions through interacting with their "neighbors of neighbors". The results and findings of this paper provide a new perspective for vaccination policy-making by taking into consideration human responses in complex social networks.