Visitor environmentally responsible behavior (ERB) is helpful for promoting the sustainable development of tourist destinations. Existing studies on visitor ERB tend to either focus on restraining visitors' environmental misconducts or rely on visitors' psychological factors. Based on the theory of engagement, this paper constructs a theoretical model to explain visitors' self-conscious ERB. Visitor engagement with the destination is investigated as an independent variable which leads to the improvement of relationship quality and visitor ERB. Relationship quality is explored to mediate the impact of visitor engagement on ERB. In addition, the moderating role of environmental clue on the tested relationships is also examined. This study adopts partial least squares structural equation modeling (PLS-SEM) to investigate a total of 410 valid questionnaires. The results show that (1) visitor engagement with the destination positively affects visitor ERB; (2) relationship quality mediates the impact of visitor engagement on visitor ERB; (3) environmental clue plays a significant moderating role in the effects of engagement and relationship quality on visitor ERB. The study extends theoretical perspectives on visitor ERB and customer engagement, and provides managerially practical value to better understand visitors' self-conscious ERB.