In minimum cost consensus problems, to accomplish the group consensus, decision makers accommodate their initial discrepant opinions based on the unit adjustment costs. During this process, decision makers may exhibit loss aversion, which results in extra expenses when participants feel loss in contrast to their reference opinion adjustments. Existing minimum cost consensus models pay little attention to the loss-averse preference. Hence, to fill up this gap, a minimum cost consensus model with loss aversion (MCCM-LA) is established and the desired properties are analyzed. To manage large-scale group decision making problems, we first propose an integrated opinion similarity, connectivity similarity and behavior similarity clustering algorithm to divide decision makers into multiple subgroups. Balancing the individual adjustment willingness and consensus reaching efficiency, a two-stage consensus reaching mechanism is further designed based on MCCM-LA to realize the accordant opinion. Finally, the effectiveness and feasibility of the proposed method are demonstrated by sensitivity and comparative analyses with an illustrative example.