This paper is to investigate the inertial dynamics of virtual-synchronous-controlled (VSynC) doubly fed induction generator (DFIG)-based wind turbines (WTs). VSynC, different from the conventional synchronization method based on phase-locked-loop (PLL) synchronizing technique, makes DFIG-based WT synchronize with power grid via the active power control (APC), and thus provide the desired inertial support to power grid. Further, an effective approach for describing the inertial dynamics of DFIG-based WT with VSynC is proposed by establishing the WT's electromechanical motion equation. The approach synthetically considers the impacts of the WT's different controller parameters, operating points, and, in particular, the variations of mechanical power caused by the rotational speed or pitch angle changes during the inertial response period. It also makes the essential of DFIG-based WT's inertia clearer, which, as a matter of fact, is controllable and manifests frequency-dependent characteristics, and noticeably differs from the fixed inertia time constant featured in synchronous generator (SG). The impacts of different controller parameters and operating points on single WT's frequency response characteristics are studied. Simulated results also validate the superiority of VSynC on inertial support capability and operation stability to the typical PLL-based vector control (VC), especially for weak grid conditions. Finally, the frequency response on wind power plant (WPP) level is initially explored and further research to improve VSynC is discussed.