The COVID-19 pandemic highlighted the intricate relationships between human health and the social-ecological system in an era of climate and global change. Widespread COVID-19 adversely affected farmers’ employment, production practices, and livelihood resilience. At the same time, climate change is a key issue limiting agricultural production worldwide. Emissions of greenhouse gases, such as carbon dioxide, are a major factor leading to global climate change. Greenhouse gas emissions from agricultural production are receiving increasing attention. Therefore, it is particularly important to develop low-carbon agriculture. Based on data from 920 family farms in Jiangsu province and Shaanxi province, this study constructs a structural equation model and empirically tests the relationship between the variables using the bootstrap method. The results show that: (1) climate change awareness did not directly stimulate farmers’ willingness to pursue low-carbon production; (2) climate change awareness has an impact on low-carbon production willingness through perceived ease of use and consequence awareness; and (3) anti-risk ability can effectively moderate the impact of climate change awareness on low-carbon production behavior in agriculture. The theoretical model framework proposed in this study provides a reference for research in the field of low-carbon agriculture and also provides some insights and suggestions for environmentalists and governments. In addition, policymakers should effectively raise the sense of responsibility of farmers to address climate change and promote low-carbon agricultural production to achieve healthy and sustainable agricultural development.