This paper presents a novel two-level Stackelberg game strategy to model the competitive relationship between power supply companies, integrated energy systems, and end users in energy trading. In the upper-level game, the power supply company acts as a leader, which stimulates the electricity purchase of the IES by adjusting the electricity price. While the integrated energy system serves as a follower, whose objective is to minimize the operational cost and determine the power purchased according to the electricity price. In the lower-level game, the integrated energy system behaves as a leader, and it sets the energy sales price on the basis of the actual energy demand of the user. As a follower, end users adjust their energy consumption strategies to balance energy purchase expenditure and energy use experience. The proposed two-level game model well describes the competition among the three participants. In order to solve the model, a distributed algorithm using alternating iterations is presented. Numeric studies have demonstrate that the developed game strategy can obtain the equilibrium solution of each participant, and can provide a good reference for energy system trading and operation.