A popular recent research trend is to investigate the feasibility of a team of cooperating UUVs (unmanned underwater vehicles). Animals group behaviour, such as fish schooling, may have lessons to offer the development of team cooperation. The goal of this paper is to justify the behaviour-based rules with fuzzy logic controlled priority weights works for team UUVs cooperation when considering dynamic manoeuvring models of an real UUV. The paper defines several behaviour-based rules to meet the requirement of a simple operational scenario. The steering angle factors generated from the rules are multiplied by the relative priority weight values and added together to make a decision on the desired vehicles' next steering angle. The priority weight values of rules are updated by the fuzzy logic method according to the situation that the vehicles meet in real time. In order to investigate the performance of the approach a dynamic manoeuvring model of a small UUV, SUBZERO III, is used to describe each vehicle in the team and a UUV cooperative mission scenario is assumed. The simulation results indicate that the entire system is successful in achieving the mission. Some parameters, such as vehicle velocity, motion update frequency, minimum distance between vehicles and minimum distance between vehicles and an obstacle, are discussed to prove that they must been specified in order to satisfy the mission requirements. From the results, we can conclude that the approach has potential for a real team of cooperative UUVs.