Measuring the vulnerability of communities in complex network has become an important topic in the research of complex system. Numerous existing vulnerability measures have been proposed to solve such problems, however, most of these methods have their own shortcomings and limitations. Therefore, a new entropy-based approach is proposed in this paper to address such problems. This measure combines the internal factors and external factors for each communities which can give the quantitative description of vulnerability of community. The internal factors contain the complexity degree of community and the number of edges inside the community, and the external factors contain the similarity degree between chosen community and other communities and the number of nodes outside the community. Considering community vulnerability from the perspective of entropy provides a new solution to such problem. Due to sufficient consideration of community information, more reasonable vulnerability result can be obtained. In order to show the performance and effectiveness of this proposed method, one example network and three real-world complex network is used to compare with some exiting methods, and the sensitivity of weight factors is analysed by Sobol' indices. The experiment results demonstrate the reasonableness and superiority of this proposed method.