Abstract: Long-term coalition of MAS has several advantages such as decreasing cost, maintaining coalition stability and improving relation. Breban and Griffiths researched trust relation among agents. But there is no feasible relation algorithm. A fuzzy relation of long-term coalition is proposed which can compute the relation value of members easily and effectively. This method reasonably describes fuzzy relation of long-term coalition. Through monitoring agent interaction, it can update the fuzzy relation. Its advantages are the decrease of computing complexity and the effectiveness improvement. It improves the work of Breban and Griffiths. The simulation result demonstrates the reliability and practicality of this method. The method is the basis of forming and evolvement research of long-term coalition and organization.