Jiangsu Province is a major industrialized province in China and its carbon emissions rank in the top five nationwide. It is of great significance to analyze Jiangsu’s carbon-peaking path for achieving China’s carbon peaking target by 2030. In this paper, based on the log-mean divisia index (LMDI) decomposition method, we calculate the main factors’ contribution to the changes in industrial carbon emissions of Jiangsu Province during 2010-2021 and reveal that the reduction in energy intensity and the optimization of energy structure will suppress industrial CO2 emissions, while the output per capita has a promoting effect on emissions. The results of the STIRPAT model fitted by ridge regression suggest that when the industrial employed population, the per capita output, and the carbon emission intensity, including technological progress, increase by 1%, the industrial CO2 emissions in Jiangsu Province increase by 0.832%, 0.602%, and 0.815%, respectively. The discrete gray model DGM (1, 1) and the scenario analysis are used to forecast the carbon emissions between 2022 and 2035. The result indicates that Jiangsu can achieve the target of significant CO2 emissions reduction without sacrificing industrial economic growth in a situation with a low population growth rate, a low per capita output growth rate, and a high carbon emission intensity reduction rate. In this case, it can reach the target of reaching the carbon emission peak by 2030 and thus lead to harmonious and sustainable socio-economic and environmental development.