Human activities largely impact the natural environment negatively, and radical changes in human societies would be required to achieve a sustainable relationship with nature. Although frequently overlooked, previous studies have suggested that supernatural beliefs can protect nature from human overexploitation via beliefs that supernatural entities punish people who harm nature. Studies of folklore and ethnology have shown that such supernatural beliefs are widely found. However, whether and how such beliefs can be maintained in human society remains a question because overexploiting natural resources without supernatural beliefs produces the greatest benefits. In this talk, we present a mathematical model based on the evolutionary game theory and derive the conditions under which supernatural beliefs can spread in society, thereby preserving natural resources. Our mathematical analysis revealed two conditions under which human society maintains supernatural beliefs and harmonizes with nature. On one hand, the fear of supernatural punishment invoked by scarce natural environments should be strong enough to prevent overexploitation; otherwise, people would continue to overuse natural resources even though they believe in supernatural punishment. On the other hand, the fear of supernatural punishment should be weak enough for the belief in supernatural punishment to spread in society via missionary events; otherwise, people would stop believing in it and be tempted to overexploit natural resources. Our results supported the idea that supernatural beliefs would facilitate sustainable relationships between human societies and nature. In particular, the study highlighted supernatural beliefs as an essential driver for achieving sustainability by altering people's interactions with nature.