This paper studies the power balance relationship and control strategy of the inter-linking converter in hybrid AC/DC microgrid in island mode under master-slave control. The main control unit bears the power fluctuation and maintain the stability of the system. The concept of capacity occupancy rate of main control unit is proposed to reflect the operation state of hybrid microgrid on both sides. According to this concept, the mathematical connection between AC and DC is established, and a partitioning control scheme for inter-linking converter is designed, which can regulate the power flow between the microgrid and achieve mutual power support between the two sides. In order to avoid the inter-linking converter switching frequently among different operation modes，hysteresis comparison is set up to improve the stability of control system. Simulation of hybrid AC/DC microgrid in PSCAD/EMTDC shows that, the control strategy of partition can realize the flexible control of the inter-linking converter and adjust the power flow between AC and DC microgrids accurately, which is helpful to realize power balance in the hybrid microgrid and maintain the stability of each sub-microgrid.