The electricity supply chain, especially electricity demand, is very sensitive to climate. Developing a clear and quantitative understanding of the impacts of climate change on monthly electricity demand is critical for long-term generation capacity planning to maintain a reliable electricity supply system. A methodological framework applicable to city-level study is proposed and applied in Tianjin to investigate the impacts of climate change on monthly electricity consumption. By combining the empirical results with an ensemble of climate predictions under three Representative Concentration Pathways (RCPs), the study simulates the changes in monthly electricity demand caused by climate change in Tianjin by the end-of-century. The simulation results showed that climate change is projected to have severe impacts on the frequency and intensity of monthly peak electricity demand. Specifically, electricity demand in July would be 56% higher than that in November in 2099 under the RCP8.5 scenario. Climate change may drive substantial changes to the electricity supply chain, and our study is indicative of a need for adaptive strategies.