For a multi-functional complementary system in the context of the energy Internet, a system operator and a user are viewed as two different behavioral bodies, and a structure of a heat and power combined supply multi-functional complementary system is built based on centrally interconnected energy hubs. Various energy supply, energy storage, and energy-using devices in a park are analyzed, refinedenergy flow models of various types of devices are established, user comfort is considered and detailed scheduling operation strategies are made for electric vehicles, household appliances, hot waterloads and air heat loads. A master-slave game model of the multi-functional complementary system is established. The model takes the minimum user energy consumption cost and maximum operator revenueas goals, and the mutual coordination of the above-mentioned energy supply, energy storage and energy-using devices is comprehensively considered. Through simulation verification, the purposes of fully exploiting the autonomy of the user, effectively taking interests of two parties into account, and realizing the interconnection and mutual benefit of an energy network can be achieved by the established model.