This paper explores a bidirectional DC-DC converter applied for a dual voltage power system using a battery and Supercapacitors. The presented converter consists of a MOSFET Full Bridge topology on the primary side of the high frequency transformer and a Current-fed Push-Pull topology on the secondary side. To reduce the device-conduction losses in the low voltage side of the converter, Synchronous Rectification is employed on both modes of charging and discharging the supercapacitors. In addition, a wide range of voltage regulation between the battery and supercapacitors is realized by the phase shift control of the full bridge and the cross ON-duty control of switches in the push-pull converter. Simulation results shows that the proposed circuit topology realizes the bidirectional power conversion with high efficiency.