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Millennial employees are increasingly paying more attention to well-being in the workplace and it has become an important issue for managers. Given that millennial employees are more sensitive to ethical issues, this study began by analyzing an ethical element in the organization—the ethical climate—and explored whether millennial employees have higher affective well-being in organizations with a good ethical climate. We verified our hypotheses based on 288 valid questionnaires collected from 40 teams. The results showed that: (1) ethical climate was a positive predictor of millennial employees’ organizational citizenship behavior (OCB) and affective well-being, (2) employees’ OCB partially mediated the relationship between ethical climate and affective well-being, and (3) an employee’s moral identity effectively moderated the relationship between ethical climate and affective well-being, although it did not play a significant moderating role between ethical climate and OCB. These findings provide empirical support for applying situational strength and social information processing theories and emphasize the importance of cultivating an ethical climate in organizations.