In this paper, the control strategy of a fully-active hybrid energy storage system, which uses two bi-directional DC/DC converters to decouple supercapacitor and battery pack from the DC bus, is proposed based on a 5th-order averaged model. Three control objectives, the battery and supercapacitor currents as well as the DC bus voltage, are regulated by using the two DC/DC converters. A Lyapunov-function-based controller is proposed to regulate the DC bus voltage to its reference value. In addition, a sliding-mode controller is designed to control the battery and supercapacitor currents to their reference values. The battery current reference is generated by the energy management strategy, while the supercapacitor current reference is generated by the Lyapunov controller to ensure DC bus voltage regulation. Simulation and experimental results show that the proposed control method has satisfactory performance, including robust tracking and a smooth transition when the load power varies in the large range. •The control strategy of the hybrid energy storage system is designed.•A Lyapunov-function-based controller is proposed to regulate the DC bus voltage.•A sliding-mode controller is designed to control battery/supercapacitor currents.•The proposed control method is verified by simulation and experimental results.