Decision makers (DMs) may exhibit non-cooperative behaviors such as deviating from recommendations or making only minor modifications in consensus-based group decision-making (GDM) problems. These non-cooperative behaviors will lead to high intra-group conflicts and low consensus efficiency. This paper designs a budget-constrained consensus framework with minimum group conflict based on social network analysis to address non-cooperative behaviors. First, the conflict degrees among DMs are quantified by opinion discrepancies and asymmetric 2-tuple linguistic trust values. Then, DMs’ weights are derived by considering degree centrality and node strength indices in the constructed conflict network. To obtain a feasible budget constraint for the consensus, the non-linear optimization models considering non-cooperative behaviors are proposed. Furthermore, two kinds of minimum conflict consensus models are established to deal with general and completely non-cooperative DMs, respectively. The existence of the optimal solutions of these consensus models and the convergence of the consensus reaching process are proved. Finally, the proposed consensus models are illustrated by an example of the negotiation of the sewage discharge standards. Compared with the consensus models based on minimum cost or adjustment, the proposed consensus models could achieve higher consensus and lower group conflict.