In group decision making (GDM), considering the individuals’ satisfaction (i.e., utilities) about the consensus result is important. However, this issue is ignored by the extant minimum cost consensus models (MCCMs). Altruism describes a way of behaving that the individuals unselfishly concern for the utilities of others. Inspired by this, in this article we discuss the minimum cost consensus problem in social network GDM (SNGDM), where the utility constraints based on altruism are first incorporated. In SNGDM, altruism is reflected as the individuals will take both their personal utility and the utilities of others who connected with them into account to form their total utility. Based on this, we first define the individuals’ altruistic utility functions in the consensus process of SNGDM, and we propose several interesting properties of the proposed utility function. Afterward, we present a novel MCCM in SNGDM with opinion dynamics and altruistic utility (MCCM-OD-AU). Notably, in the proposed model, the deviation of opinion adjustment in the consensus process is measured as a psychological distance perceived by the individuals. Furthermore, some simulation studies and comparative analysis are conducted to investigate the effects of the altruistic behavior and the psychological distance of opinion adjustment on the consensus reaching results. Finally, two numerical studies, including an illustrative example and an application in energy-saving target formulation with real-world social network data, are provided to justify the performance of our proposal.