A Modular Multilevel Converter-based High-voltage Direct Current (MMC-HVDC) can provide power to important areas such as island power grids. When island power grids are in the process of active and passive network switching, there are problems of instability such as active power imbalance and AC voltage oscillation. Therefore, an active/passive switching control strategy for an MMC-HVDC connected to an island power grid is proposed. This control strategy is optimized for outer loop power control and phase angle control. These eliminate the instantaneous active power imbalance of the island power grid at the moment of active/passive network switching, and can achieve a smooth switching of the island power grid. Finally, a three-phase MMC simulation model is built in PSCAD/EMTDC. The simulation results show that under the action of the proposed control strategy, the system can operate normally at the time of active, passive and both switching times. The results verify the effectiveness and correctness of the proposed control method. This work is supported by National Natural Science Foundation of China (No. 51777216) and Natural Science Foundation of Shandong Province (No. ZR2018MEE040 and No. ZR2019MEE094).