The low-carbon power transition, which is key to combatting climate change, has far-reaching effects on achieving the Sustainable Development Goals (SDGs) in terms of issues such as resource use, environmental emissions, employment, and many more. Here, we assess the potential impacts of the power transition on progress toward achieving multiple SDGs (covering 18 targets across the 17 goals) across 49 economies under nine socioeconomic and climate scenarios. We find that the low-carbon power transition under the representative concentration pathway (RCP)2.6 scenarios could lead to an approximately 11% improvement in the global SDG index score from 54.70 in 2015 to 59.89-61.33 in 2100. However, the improvement would be significantly decreased to 4.42%-7.40% and 7.55%-8.93% under the RCP6.0 and RCP4.5 scenarios, respectively. The power transition could improve the overall SDG index in most developed economies under all scenarios while undermining their resource-related SDG scores. Power transition-induced changes in international trade would improve the SDG progress of developed economies but jeopardize that of developing economies, which usually serve as resource hubs for meeting the demand for low-carbon power transition in developed economies.