Understanding the socially influenced decision-making process that determines voluntary vaccination is essential for developing strategies and interventions of vaccine-preventable diseases. Both theoretical and experimental studies have suggested that a variety of factors, such as safety of vaccines, severity of diseases, information and advice from healthcare professionals, influence an individual's intention to vaccinate. However, limited research has been conducted on analysing systematically how individuals’ vaccine acceptance decisions are made from their beliefs and judgements on the influential factors. In particular, there is lack of quantitative analysis on how individuals’ beliefs and judgements may evolve from the spreading of vaccination-related information in a social network, which further affects their decision making. In this paper, an integrated model is first proposed to characterise the socially influenced vaccination decision-making process, in which each individual's beliefs and subjective judgements on the decision criteria are formulated as belief distributions in the framework of multiple criteria decision analysis (MCDA). The spreading of social influence in the network environment is further incorporated into the information aggregation process for supporting informed vaccination decision analysis. A series of simulation-based analyses on a real-world social network is conducted to demonstrate that the overall vaccination coverage is determined primarily by individuals’ beliefs and judgements on the decision criteria, and is also affected sensitively by the characteristics of influence spreading (including the content and amount of vaccination-related information) in the social network.