In response to global climate change, China has committed to peaking carbon emissions by 2030 and achieving carbon neutrality by 2060, commonly known as the “30–60 Dual Carbon”. Under the background of “30–60 Dual Carbon”, this article takes the electric power industry, which is the main industry contributing to China’s carbon emission, as the research object, explores the time and peak value of the carbon peak of the electric power industry, and analyzes whether carbon neutrality can be realized under the peak method, so as to get the carbon neutrality path of the electric power industry and serve as the theoretical basis for the formulation of relevant policies. The Environmental Kuznets Curve inspection and the relationship analysis are carried out, then the system dynamics model is constructed, the carbon emissions from 2020 to 2040 are simulated, and the peak time is predicted. Three different scenarios are set to explore the path of electricity carbon neutralization under the premise of a fixed peak. It is shown that Gross Domestic Product per capita index factors have the largest positive contribution, and thermal power share index factors have the largest negative contribution to electricity carbon emissions. Based on the current efforts of the new policy, carbon emissions can achieve the peak carbon emissions’ target before 2030, and it is expected to peak in 2029, with a peak range of about 4.95 billion tons. After the power industry peaks in 2029, i.e., Scenario 3, from coal 44%, gas 9% (2029) to coal 15%, gas 7% (2060), where the CCUS technology is widely used, this scenario can achieve carbon neutrality in electricity by 2060. Adjusting the power supply structure, strictly controlling the proportion of thermal power, optimizing the industrial structure, and popularization of carbon capture, utilization, and storage technology will all contribute to the “dual carbon” target of the power sector.