In the context of the launch of the carbon market, power producers need to participate in both the carbon and electricity markets, which can affect the equilibrium of electricity market. In order to study the trading decisions of power producers in the carbon and electricity markets and the interactive influence relationship between these two markets, a two-layer equilibrium model for the oligopoly electricity market considering carbon market trading, which considers the gaming behaviors of power producers in the electricity and carbon markets. For the established model, the co-evolutionary algorithm is used to solve the Nash equilibrium. Finally, the validity of the relevant models and algorithms is verified via case studies, and the impacts of the carbon market on the equilibrium of electricity market and the gaming behavior of the power producers market are mainly studied. The results show that, in the current case of using the baseline method for initial carbon allowance allocation, the strategic behaviors of power producers raise both the electricity and carbon prices, where the increase amplitude of electricity prices is much smaller than the increase of carbon prices.