Decarbonization policies worldwide encourage the use of renewable energy to generate electricity and electrify transport. In line with these policies, the use of energy storage systems in electric vehicles can support the integration of renewable energy as a resource called V2G (vehicle to grid). This system of equipment has a problem because the energy it produces can't be directly injected back into the grid. An essential element of the V2G system is the bidirectional converter which can charge and discharge EV batteries. Research related to bidirectional converters has been developed a lot. One of these converter topologies that have a wide output voltage range and smaller current ripple is the H-bridge bidirectional converter. In addition to the type of converter topology that must be selected, a current control method that can respond to dynamic changes quickly, accurately, and is simple to implement is also very important. Using fuzzy logic, this research aims to control the DC-DC current converter with adaptive hysteresis bandwidth. On the other hand, the adaptive HB variable is expected to limit MOSFET performance at high and irregular frequencies that make switching losses and frequency noise. To improve the quality of the output current, frequencies are limited. Simulations were conducted using PSIM and co-simulation with Simulink to validate the proposed control performance. The results show fuzzy logic is a good method to make an HB adaptive and the frequencies were around 9.23 k H z ≤ f ≤ 9.49 k H z. It is very possible to make the microcontroller and MOSFET work according to the work frequency capabilities.