The world is moving towards a greener economy, a more equal society and better governance under the Sustainable Development Goals (SDGs) and the “Environmental, Social and Governance” initiative. Doubts remain on whether a greener economy and better governance are helpful in achieving income equality. This study aims to examine the relationship between green economy, governance and income inequality, applying quantile regression to capture the different relationships in different levels of income inequality between 2009 and 2019 in 30 countries. The results reveal that green economy proxies are mostly not significant in high-income countries but can aggravate income inequality in middle-income countries at lower quantiles to create a green economy-income inequality trap. Better governance can reduce inequality in high-income countries but worsen inequality in middle-income countries. The findings imply that high-income countries can pursue a sustainable green economy without needing to be concerned about income inequality, which is reduced only with better governance. In contrast, good governance is harmful to income inequality in middle-income countries. It hints at serious fundamental flaws in institutional structure. These are urgent challenges in policy formulation and economic planning regarding the SDGs towards achieving the sustainability trinity of lowering inequality, a greener economy and better governance.