Coalition stability is an important concept in coalition formation. One common assumption in many stability criteria in non-transferable utility games is that the preference of each agent is publicly known, so that a coalition is said to be stable if there is no objections by any sub-group of agents according to the publicly known preferences. However, in many applications including some software agent applications, this assumption is not realistic. Instead, intelligent agents are modeled as individuals with private belief and decisions are made according to those beliefs instead of common knowledge. Such belief based agents architectures have impacts on the coalition’s stability which are not reflected in the current stability criteria. In this paper, we extend the classic stability concept of the core by proposing a new belief based stability criterion which we labeled the belief-based core, and give examples to illustrate how the new concept can be used to provide both ex-ante and ex-post analysis of coalition formation mechanism.