In this paper, we first propose a fractional-order energy demand–supply system, with the background of the energy resources demand in the eastern regions of China and the energy resources supply in the western regions of China. Then, we confirm the energy resource attractor with a necessary condition about the existence of chaotic behaviors. By employing an improved version of Adams Bashforth Moulton algorithm, we use three cases with different fractional values to verify the necessary condition. Finally, chaos control of fractional-order energy demand–supply system is investigated by two different control strategies: a linear feedback control and an adaptive switching control strategy via a single control input. Numerical simulations show that the energy demand and import in Eastern China and energy supply in Western China are self-feedback controlled around the system’s equilibrium point.