Climate change is a challenge facing all countries around the world. In response to the global climate change, China has pledged a two-stage carbon reduction goal of “dual carbon” to realize sustainable development. Industrial structure upgrading driven by green finance is an important way to reduce carbon emissions and achieve sustainable development. In this work, we investigate the impact of green finance on promoting industrial structure upgrading in Jiangsu province. We construct the grey correlation degree and coupling coordination degree model to analyze the relationship between green finance development and industrial structure upgrading with data from 13 prefecture-level cities in Jiangsu province from 2010 to 2021. The results demonstrate that green finance policies inhibit the financing tendencies of high-energy consumption industries and improve the financing difficulties of high-energy enterprises, forcing high-energy industries to transform and realize industrial upgrading. In addition, the improvement in green energy consumption structure and energy production efficiency will promote an improvement in carbon emission efficiency. Moreover, the development of green finance contributes to promoting industrial structure upgrading, putting forward new requirements for the development of green finance as well. Furthermore, the promotion of green finance and low-carbon industries provides a strong driving force for industrial structure upgrading as well as high-quality economic development in Jiangsu province. Therefore, the green finance policy system, as well as innovation in green financial products, needs to be further improved to accelerate industrial structure upgrading.