For the stable operation of a grid, the voltages of all buses in the grid should be maintained within an acceptable range. For a grid with high wind penetration, wind power plants (WPPs) are required to have the capability to maintain the voltage at the point of common coupling (PCC). Wind generators in a WPP produce the different active power due to the wake effects and consequently contain different reactive power availability. This paper proposes a voltage control scheme of a doubly-fed induction generator (DFIG)-based WPP using the adaptive reactive power-voltage (Q-V) characteristic of DFIGs. The WPP controller calculates a voltage error signal using a PI controller and sends it to each DFIG. From the voltage error signal, the DFIG injects the reactive power based on its adaptive Q-V characteristic, which depends on the available reactive power. The proposed scheme adjusts the Q-V characteristic depending on the operating condition of a DFIG. The proposed scheme enables the WPP to recover the PCC voltage to the nominal value within a short time after a disturbance by utilizing the reactive power capability of a WPP. The performance of the scheme was investigated for a 100 MW WPP consisting of 20 units of a 5 MW DFIG for a grid fault condition. The results show the proposed scheme successfully recovers the PCC voltage within a short time after a disturbance.