Driven by the“dual carbon”goal, significant changes will occur in social and economic development, energy production, and consumption structure, leading to new characteristics in factors and trends affecting electricity de-mand forecasting. The power industry is a key area to ensure the practical achievement of the“dual carbon”goals, so research needs to be conducted on electricity demand forecasting method under the new situation. Logarithmic mean index method（LMDI）and path analysis method are used to study the influencing factors of electricity demand under the background of“dual carbon”, and extracts three carbon emission related influencing factors of electricity demand：electrification rate, clean energy generation ratio, and energy intensity. A method for predicting electricity demand based on fuzzy autoregressive distributed lag model is proposed. The regression coefficients are fuzzified on the basis of the autoregressive distributed lag model considering policy lag effects. By establishing a mini-mum fuzziness optimization model, the regression parameters with the least uncertainty are obtained, which improved the accuracy of long-term electricity demand prediction under the background of “dual carbon”. Based on the historical data of China’s socio-economy and electricity demand, and in combination with the national policy objectives, the electricity demand in China under different low-carbon paths has been predicted to verify the feasibility and effectiveness of the power demand forecasting method proposed in this article.