Recently, large-scale group decision making (LSGDM) in social network comes into being. In the practical consensus of LSGDM, the unit adjustment cost of experts is difficult to obtain and may be uncertain. Therefore, the purpose of this paper is to propose a consensus model based on robust optimization. This paper focuses on LSGDM, considering the social relationship between experts. In the presented model, an expert clustering method, combining trust degree and relationship strength, is used to classify experts with similar opinions into subgroups. A consensus index, reflecting the harmony degree between experts, is devised to measure the consensus level among experts. Then, a minimum cost model based on robust optimization is proposed to solve the robust optimization consensus problem. Subsequently, a detailed consensus feedback adjustment is presented. Finally, a case study and comparative analysis are provided to verify the validity and advantage of the proposed method.