With the continuous promotion of energy market, the interaction of energy entities in regional comprehensive energy system is deepening. As the link of multiple energy conversion, transmission and transaction, energy hub realizes the coupling between different energy entities. In this context, this paper proposes an optimization strategy based on multi-energy game interaction between supply and demand of energy hub. Firstly, a bilateral game model of energy hub supply and demand is established, in which energy purchasing game is conducted with energy dealers on the supply side and energy sales game is conducted with users on the demand side. Secondly, it is proved that the game model has a unique Nash equilibrium solution. Finally, the results of an example show that the proposed model has good convergence. The two-sided game of supply and demand involving multiple energy sources can make the income of energy distributors and energy hubs higher. At the same time, the introduction of energy storage equipment is conducive to realize the coordinated operation of source-load-storage.