Abstract: To improve the frequency stability of power systems after being subjected to a major disturbance, the wind turbine（WT） is required for the ability of active frequency support. However, the existing WT frequency support control is mostly a direct imitation of the inertia and frequency regulation characteristics of synchronous generators, which limits the control flexibility of the WT. Given this deficiency, originating from the core demand for improving the frequency nadir, an optimal frequency support control of the WT is proposed, which considers the primary frequency regulation characteristics of the system. First, with the control objective of maximizing the frequency nadir, the general form of the optimal system frequency trajectory is proposed and strictly proven. Then, the quantitative expression of the energy recovery characteristics of the WT is constructed, and the optimal frequency support control of the WT is deduced reversely by combining the system frequency response model. Finally, the simulation and comparison results demonstrate that the proposed method significantly improves the frequency nadir by cooperating with the original frequency regulation characteristics of the system, and shows better robustness to different operation conditions and power disturbance levels.