Aiming at the problem of global climate change and energy crisis, wind power has become the focus of energy sustainable development in all countries. The wind turbines (WTs) power system is connected to the grid via the power electronic converter, causing the system inertia level to drop. In this paper, the direct-drive WT system is considered as the research object, and the whole-system frequency response model is established. The inertia and damping characteristics of the WT converter systems with virtual inertia control are analyzed. With the support of fan rotor kinetic energy and the energy saved in a capacitor, the simple control can also make the system exhibit different degrees of inertia and damping features. The results show that the equivalent inertia and the WT inertia time constant, capacitance parameters and virtual control parameters kd are related; the equivalent damping parameter is related to the steady-state operating point parameters and the virtual control parameter kp; the equivalent synchronization parameter is related to the steady-state operating point parameters and the virtual inertia control parameter ki. Finally, the correctness of the inertial and damping characteristics of the WT grid-connected system is verified by simulation, which provides a theoretical reference for studying the inertial damping of power electronic dominant systems.