This paper proposes a power sharing control method for the bidirectional AC/DC power converter (BPC) in a hybrid microgrid. The hybrid microgrid is composed of AC subgrids and DC subgrids interconnected by BPC. The studies concentrate on the grid-off mode. When the microgrid operates in grid-off mode, the BPC is expected to be a balancer to guarantee the power supply quality for the two subgrids. The proposed control method can realize proportionally power sharing between the AC subgrid and DC subgrid, based on the capacity of each device. For better control performance, the square of DC bus voltage is used instead of DC voltage, which can make the control of DC bus voltage more linearized and improve the dynamic response of the DC bus voltage. Theoretical analysis and modeling are provided. The feasibility of the proposed method is validated by simulations in MATLAB\Simulink software.