A simple model was built to predict the national and regional electricity demand by sectors under China’s new normal situation. In the model, the data dimensionality reduction method and the Grey model (GM(1,1)) were combined and adopted to disaggregate the national economic growth rate into regional levels and forecast each region’s contribution rate to the national economic growth and regional industrial structure. Then, a bottom–up accounting model that considered the impacts of regional industrial structure transformation, regional energy efficiency, and regional household electric consumption was built to predict national and regional electric demand. Based on the predicted values, this paper analyzed the spatial changes in electric demand, and our results indicate the following. Firstly, the proposed model has high accuracy in national electricity demand prediction: the relative error in 2017 and 2018 was 2.90% and 2.60%, respectively. Secondly, China’s electric demand will not peak before 2025, and it is estimated to be between 7772.16 and 8458.85 billion kW·h in 2025, which is an increase of 31.28–42.88% compared with the total electricity consumption in 2016. The proportion of electricity demand in the mid-west regions will increase, while the eastern region will continue to be the country’s load center. Thirdly, under China’s new normal, households and the tertiary industry will be the main driving forces behind the increases in electric demand. Lastly, the drop in China’s economy under the new normal will lead to a decline in the total electricity demand, but it will not evidently change the electricity consumption share of the primary industry, secondary industry, tertiary industry, and household sector.