Carbon market trading increases the cost of power generation of traditional fossil energy units, and then affects their bidding behavior in the electricity market, as well as the electricity market equilibrium. In this paper, a two-layer equilibrium model is established for the electricity market equilibrium problem under the background of carbon market. The upper model is the optimal bidding model of the electricity generator considering the carbon emission cost and the lower model is the power market clearance model considering the total constraint of the carbon quota. Then, the two-layer model is transformed into a mixed integer linear programming problem by using optimality condition theory and linearization methods such as binary expansion approach and big M method. Finally, based on the PJM 5-node system, the equilibrium of electricity market with and without carbon market in multi-market environment are solved, and the influence of carbon market on electricity market equilibrium state is analyzed. At the same time, based on the sensitivity analysis total carbon quota to electricity market equilibrium, it is found that the total carbon quota needs to be appropriately tightened to achieve the maximum effect of electricity low-carbon emission reduction.