In this paper, we aim to analyze how to effectively promote compliance management in the electricity market. We construct an evolutionary game model under the two different scenarios, i.e., the scenario without governmental supervision and the scenario with governmental supervision, and explicitly describes the strategic behaviors and dynamic evolution process of power enterprises and regulators in the power market. According to the results of the evolutionary stable strategy, we find that, in the absence of governmental supervision, the long-term stable equilibrium of power enterprises' choice of strategy “Compliance” and regulatory agencies' choice of strategy “Not bribery” is hard to be realized. Only if the government effectively supervises the compliance management of the electricity market can the ideal compliance behavior of the two stakeholders be achieved. Furthermore, we conduct a simulation study to analyze the impacts of the various model parameters on the dynamic evolution process. The specific results show that the lower compliance cost, the higher psychological cost, and the larger profit loss of the power enterprises, as well as the lower inspection cost, the higher psychological cost, and the larger rewards of the regulatory agencies, can promote the formation of compliance management. Besides, the larger penalty charged by the government is also conducive to the compliance management of the electricity market.