The purpose of this study is to explore the relationship between social responsibility and risk in international construction projects using corporate reputation and customer satisfaction as mediating variables. This study collected 141 valid data using the questionnaire method and used partial least squares structural equation modeling (PLS-SEM) and fuzzy set qualitative comparative analysis (fsQCA) to analyze the data. The PLS-SEM results showed that, in international construction projects, social responsibility has no direct impact on risk but has a positive impact on corporate reputation and customer satisfaction. Customer satisfaction mediated the relationship between social responsibility and risk in international construction projects, but corporate reputation did not mediate this relationship. This study also found that corporate reputation and customer satisfaction have a serial mediating role in this relationship. In addition, the fsQCA results further confirmed that improving customer satisfaction is a necessary condition for mitigating risks in international construction projects. In terms of the different dimensions of social responsibility, the protection of shareholders’ rights is a core condition for mitigating risks in international construction projects. This study provides useful insights for international construction project managers to develop risk mitigation plans from the perspective of social responsibility.