This article proposes an adaptive-output-voltage-regulation (AOVR)-based solution to alleviate the dc-link undervoltage for grid-forming (GFM) inverters. First, it is shown that large disturbances may cause the dc-link undervoltage for GFM inverters threatening the safe operation of the system. To tackle this issue, an AOVR-based control strategy is proposed, whose main idea is to reduce the output voltage of the GFM inverter and also speed up the dynamic process of the power angle by intentionally enlarging the frequency deviation of the active power control loop. By doing so, the dc-link output energy will reduce to avoid possible undervoltage. The parameter design of the proposed method is based on the overmodulation constraints, and an auxiliary module is configured for the low-voltage-ride-through (LVRT) requirements. The applicability of the proposed solution is checked when considering the current limitation. The pros of the proposed solution are also depicted when compared with state-of-art solutions. The effectiveness of the proposed control strategy is finally confirmed by the experimental tests.