Engineering designers are crucial professionals to put green principles into practice to improve the green performance of engineering projects. The social context and personal values of designers are more likely to stimulate their initiative and voluntary conduct for green design and induce more persistent behavior changes. Thus, this research, from a social-psychological perspective, investigated how designers’ social relationships work on green design intention by assessing the roles of personal norms and voluntary instruments. Then, using the data collected by a questionnaire survey, Partial-Least Squares Structural Equation Modeling was employed to validate theoretical hypotheses. The results show that designers’ social relationships positively correlate with their green design intention and personal norms, and personal norms partially mediate the relationship between social relationships and green design intention. Furthermore, the strong effectiveness of voluntary instruments helps strengthen the influence of social relationships on green design intention. The findings of this study imply that enhancing social relationships is an effective way to activate designers’ personal norms and encourage their green intention and that appropriately utilizing voluntary instruments is also beneficial. This research is valuable for the green development of the engineering design industry.