Greenwashing is an obstacle to the sustainable development of society, but the current governance of greenwashing is still a “common” governance, not a “collaborative” governance. Accordingly, this study focuses on the three stakeholders of greenwashing governance: company, media and government. Using a sample of listed companies that have published social responsibility reports from 2014 to 2018, this study analyzes the influence mechanism of media reports on greenwashing and discusses the moderating role of government regulation and mediating role of internal supervision. This study finds that internal supervision plays a hiding role in the process of media reports reducing greenwashing, but government regulation has a weakening effect on this hiding effect, showing a “common” governance. Simultaneously, this “common” governance is heterogeneous across time (i.e., corporate life cycle), space (i.e., spatial spillovers) and environment (i.e., the uncertainty of corporate external policies). However, when the cooperation between the government and the media is strengthened, the hiding behavior of the companies is suppressed and the performance of greenwashing governance is improved, so that “collaborative” governance is achieved. Against this backdrop, this study provides a macro‐to‐micro governance policy framework for corporate greenwashing from the four dimensions of strategy, systems, tools, and information to achieve “collaborative” governance. This study enriches the research on the corporate greenwashing governance and has practical implications for the government, media and other stakeholders.