The achievement of the carbon peaking and carbon neutrality targets requires the adjustment of the energy structure, in which the dual-carbon progress of the power industry will directly affect the realization process of the goal. In such terms, an accurate demand forecast is imperative for the government and enterprises’ decision makers to develop an optimal strategy for electric energy planning work in advance. According to the data of the whole social electricity consumption in Jiangsu Province of China from 2015 to 2019, this paper uses the improved particle swarm optimization algorithm to calculate the fractional-order r of the FGM (1, 1) model and establishes a metabolic FGM (1, 1) model to predict the whole social electricity consumption in Jiangsu Province of China from 2020 to 2023. The results show that in the next few years the whole social electricity consumption in Jiangsu Province will show a growth trend, but the growth rate will slow down generally. It can be seen that the prediction accuracy of the metabolic FGM (1, 1) model is higher than that of the GM (1, 1) and FGM (1, 1) models. In addition, the paper analyzes the reasons for the changes in the whole society electricity consumption in Jiangsu Province of China and provides support for government decision making.