In order to realize the reliable grid connection of an AC/DC hybrid microgrid, a control strategy for a bidirectional AC/DC interlinking converter connected to an AC-DC subnet in a hybrid microgrid is proposed based on a droop control strategy in the microgrid and a pre-synchronization working principle. In the island/grid-connected mode, the bidirectional droop control is used to achieve bidirectional power flow. When the island mode is changed to the grid-connected mode, the amplitude and phase synchronization can be realized by eliminating the voltage deviation of the dq axis without obtaining phase information through phase-locked loop to realize smooth grid-connection. At the same time, for the three-phase unbalanced conditions caused by an unbalanced load in the microgrid, the method of positive and negative sequence control is adopted to realize the synchronous interconnection of the microgrid under non-ideal conditions. Simulation results verify the feasibility of the proposed scheme. This work is supported by Natural Science Foundation of Shanxi Province (No. 201701D121134), National Natural Science Foundation of China (No. U1610121) and Science and Technology Grant Program of Shanxi Province (No. 20181102028).