This paper 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, where the 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 also checked when considering the overcurrent limitation. The effectiveness of the proposed control strategy is finally confirmed by the experimental tests.