The growing concerns of environmental degradation call for attaining higher green growth (GRG) in both developing and developed countries. Therefore, achieving a higher GRG has been a main concern of policymakers worldwide. To this end, a comprehensive policy framework is needed to attain higher level of GRG and sustainable development goals (SDGs). In doing so, this study is an earliest attempt that investigates the impact of economic policy uncertainty, green innovation and financial development on GRG using the data of selected fragile countries during 1996–2019. For this purpose, we use different preliminary tests for checking the reliability of the data and panel quantile regression for testing the association among the variables. The empirical results indicate that economic policy uncertainty, green innovation and financial development contribute to the growth of green economy. The positive association of economic policy uncertainty with GRG is due to the decline in investment and overall energy consumption pattern. Based on the empirical results, this study proposes some policy implications to achieve higher level of GRG and different targets of SDG 08 (economic growth), SDG 09 (innovations), and SDG 13 (climate change).