In the context of the new normal, the global economy is entering a deep adjustment period, and the driving forces of development are also constantly changing. As a result, China’s economy has also entered a “new normal” phase in which it is growing in a manageable and relatively balanced manner. In addition, the new normal characteristics of the power industry’s development in China are also very significant, and they affect the adaptability of traditional power forecasting methods. By analyzing the new characteristics of China’s economic development and the changing electricity demand in recent years, this paper quantitatively studied the effect of the national economy on the consumption of electricity. Meanwhile, a modified logistic model based on the change of the gross domestic product (GDP) growth rate is constructed to make a reasonable prediction of the future power consumption in China. Subsequently, by calculating the elasticity of electricity consumption in the future, it is found that the coefficient decreases each year, which indicates that electricity consumption in China is following a new trend. Based on the research results, this paper proposes rational suggestions for China’s power development, and they are expected to provide references for the power planning and power industry layout in China.