Operation delay of DC circuit breakers causes a voltage sag of several milliseconds in high-voltage DC (HVDC) grids. The DC voltage sag can cause an overcurrent in the DC side of the modular multilevel converter (MMC), resulting in halting the MMC. This study investigates a method to facilitate continuous operation of the half-bridge MMC during a DC voltage sag. The proposed method performs feedback control of the DC current during DC voltage sags by decreasing the DC and AC voltages of the half-bridge MMC. When the method is applied to symmetrical monopole HVDC systems, the MMC can maintain both its DC and AC currents within the rated range during the voltage sag caused by pole-to-ground faults. Simulation results obtained by a three-terminal HVDC grid verify the DC fault ride-through capability of the half-bridge MMC.