Considering multiple end-users taking part in the electric power market transaction of the smart grid, an energy trading market model of multiple end-users is constructed by introducing the double auction mechanism in this paper firstly. Then the model is transformed into a non-cooperative game model with incomplete information. To make energy trading among multiple users tend to be stable, an adaptive learning algorithm is proposed for the end-users playing the game to find the optimal mixed-strategy based on the Q learning, and the overall game comes up to Nash equilibrium, so that energy trading between the multiple end-users can run stably. Finally, the probability distribution of mixed-strategy for multiple end-users to obtain Nash equilibrium under numerical simulation, the validity of the proposed energy trading algorithm is verified.