In islanded mode, an AC/DC hybrid microgrid can realize power mutual support between the AC microgrid and the DC microgrid through an interlinking converter (IC). There is a problem in that the IC adopting the traditional droop control and the current control method based on proportional-integral (PI) has small inertia and poor dynamic performance in the islanded mode. Thus a novel control strategy based on a virtual synchronous generator (VSG) is proposed. First, based on traditional droop control, the improved VSG control method is proposed by introducing the difference of AC frequency and DC voltage to improve the stability of the system voltage and frequency. Then, in the current loop of the IC, fixed time sliding mode control (SMC) is proposed to improve the dynamic performance of the system. Next, power secondary control is introduced into the AC and DC microgrids to realize system voltage and frequency recovery. Finally, an AC/DC hybrid microgrid model built on the StarSim hardware-in-the-loop real-time simulation platform verifies that the proposed novel control strategy can realize power mutual support between AC/DC microgrid subsystems, improving system inertia and dynamic control performance.