The small-signal stability (SSS) of the doubly-fed variable-speed pumped storage plant (VSPSP) is analysed based on the impedance modelling and Individual Channel Design (ICD) framework. There exists couplings between the d and q frame in the impedance model of doubly-fed induction machine (DFIM), which have a significant influence on the stability. Considering that the couplings are hard to reduce in different domains, this paper apply a more transparent ICD framework instead of the widely used Generalized Nyquist Criterion (GNC) to analyse the SSS of VSPSP. Firstly, the impedance model of DFIM in d-q domain is derived through transfer matrix. Then two single input single output (SISO) channel transmittances, which represent the dynamics of d-q frame respectively, are reformulated based on ICD. Therefore, the classical Nyquist/Bode analysis is utilized in the individual channels. It is proved that the ICD can preserve the loop interactions in the individual channels although the cross-coupling is strong. The influences of electrical and control parameters as well as operating mode on the SSS of DFIM based VSPSP are analysed, and the structural robustness of the channels are evaluated. The results show that the system is more prone to instability in pump mode.