For the fixed-gain inertial control of wind power plants (WPPs), a large gain setting provides a large contribution to supporting system frequency control, but it may cause over-deceleration for a wind turbine generator that has a small amount of kinetic energy (KE). Further, if the wind speed decreases during inertial control, even a small gain may cause over-deceleration. This paper proposes a stable inertial control scheme using adaptive gains for a doubly fed induction generator (DFIG)-based WPP. The scheme aims to improve the frequency nadir (FN) while ensuring stable operation of all DFIGs, particularly when the wind speed decreases during inertial control. In this scheme, adaptive gains are set to be proportional to the KE stored in DFIGs, which is spatially and temporally dependent. To improve the FN, upon detecting an event, large gains are set to be proportional to the KE of DFIGs; to ensure stable operation, the gains decrease with the declining KE. The simulation results demonstrate that the scheme improves the FN while ensuring stable operation of all DFIGs in various wind and system conditions. Further, it prevents over-deceleration even when the wind speed decreases during inertial control.