Electricity sector is sensitive to climate change. In this study, a fixed-effect regression feedback model is used to estimate the impacts of climatic factors on electricity demand in China by using panel data of 30 provinces from 1995 to 2016. We also forecast the potential impacts of climate change on future electricity demand under three climate change scenarios. The results show that (1) there is a positive effect of the heating degree day (HDD) and cooling degree day (CDD) on the per capita electricity demand. A 1% increase in the CDD will result in a 0.094% increase in per capita electricity demand, while the same rise of HDD will increase per capita electricity demand by 0.061%. In addition, the per capita electricity demand will decrease by 0.017% if the sunshine duration increases 1%, while the effect of rainfall is not significant. (2) The total changes in electricity demand caused by climatic factors by 2100 under the RCP2.6, RCP4.5, and RCP8.5 scenarios will be 69.52 billion kWh, 222.74 billion kWh, and 518.58 billion kWh, representing 1.0%, 3.53%, and 8.53% of the total electricity consumption in China in 2017, respectively. The effect of climate warming on China’s electricity demand is apparent.