Conflict analysis and resolution provide effective decision support for management problems with uncertainty and inconsistency. Conflict refers to the multi-agents' inconsistent attitudes towards issues of common concern. Conflict analysis aims to find the intrinsic causes of conflict to find consensus strategies. And agents in the conflict situation constitute a social network. Trust relationship plays a crucial role in the social network. In this paper, we introduce trust mechanism in the conflict analysis under the framework of granular computing to investigate the impact of trust relationship on the conflict situation. And we propose a theoretical model for conflict detection and elimination that integrates agent's influence and conflict coefficient of quantitative three-way opinion subsets (CC-OS). We achieve conflict detection and elimination through four stages: trust propagation process, consensus willingness reaching, determine agent's weight and conflict detection and elimination. We illustrate the proposed model and method by analyzing a realistic conflict problem and verify the effectiveness and superiority of the model. The main contribution of this paper is twofold. One is to make a new theoretical contribution to multi-agents conflict analysis from the perspective of trust social network. Another is to provide a more quantitative basis for specific conflict analysis and decision-making.