Abstract: The impedance method is a hotspot for studying the subsynchronous oscillation of wind power systems. The frequencydomain impedance criterion adopted by the impedance method judges the stability of the system according to the positive or negative resistance when the reactance is at the zero-crossing point. The criterion is simple but lacks theoretical proof. This paper discusses the relationship between the frequency-domain impedance criterion and the Lyapunov’s first method to determine the system stability according to the impedance solution method based on the state space. It is proven that the impedance method and the Lyapunov’s first method have the same stable boundary. There are two cases of the impedance criterion in the non-boundary case, and the frequency-domain impedance criterion in the existing literature is applicable to one of the cases. At this time, the impedance criterion and the Lyapunov’s first method have the same stability judgment result, but have different oscillation frequencies. Further, the application scope of the impedance criterion is discussed. Finally, based on two wind power system examples, the correctness of the impedance criterion in two cases is verified.