<p>Due to the lack of external grid support, the off-grid wind-hydrogen production system has problems such as low system inertia, susceptibility of DC bus voltage to load fluctuations and AC/DC faults during operation. The stability of DC bus voltage is of great significance for maintaining system stability and ensuring the normal operation of various equipment in the hydrogen production system. Therefore, improving the control strategy of the AC/DC converter of the wind turbine to provide inertial support for the system is of great significance for maintaining system stability. By analogy with existing AC virtual synchronous machine control, this paper introduces a DC virtual inertia control strategy to improve the inertia of the system. And based on this, a DC virtual inertia controller based on extended state observer (ESO) and global fast terminal sliding mode control (GFTSMC) is proposed to improve control effect. This controller is applied to the generator side converter of the direct-drive wind turbine to support the DC bus voltage. A simulation model of the DC off-grid hydrogen production system was built in the DIgSILENT. The simulation results show that this control strategy has excellent control effect on the DC bus voltage and provides inertial support for the DC off-grid hydrogen production system.</p>